THE  ECLIPSING  BINARY  SIGMA  AQUILAE, 
THE  CEPHEID  VARIABLE  ETA  AQUILAE 


By 

CHARLES  CLAYTON  WYLIE 

A.  B.  Park  College,  1908 

A.  M.  University  of  Missouri,  1912 


THESIS 

SUBMITTED  IN  PARTIAL  FULFILLMENT  OF  THE  REQUIREMENTS  FOR  THE 
DEGREE  OF  DOCTOR  OF  PHILOSOPHY  IN  ASTRONOMY  IN  THE 
GRADUATE  SCHOOL  OF  THE  UNIVERSITY  OF 
ILLINOIS,  1922 


URBANA,  ILLINOIS 


Digitized  by  the  Internet  Archive 
in  2015 


https://archive.org/details/eclipsingbinarysOOwyli 


1 0 

W9t 


UNIVERSITY  OF  ILLINOIS 


THE  GRADUATE  SCHOOL 


1922 


I HEREBY  RECOMMEND  THAI'  THE  THESIS  PREPARED  UNDER  MY 


SUPERVISION  BY Charles  Clay tozY.lyli5 


ENTITLED^  .The__.Eolip8lng  Binary  SigsiaLAq^ilae.^ 


The  _Cephe  1 d_  Variable  ta  Aquilae, 


BE  ACCEPTED  AS  FULFILLING  THIS  PART  OF  THE  REQUIREMENTS  FOR 


THE  DEGREE  OF. 


Doctor  of  Philosophy 


In  Charge  of  Thesis 


Head  of  Department 


Recommendation  concurred  in* 


y. 

•Required  for  doctor’s  degree  but  not  for  master’s 


Committee 


on 


Final  Examination* 


CS8S99 


' .^'Q  ^ it* *i  r o 3 ns.j/-i  .-M  If 

‘SS0^-'M'r  ' B .m  tj: 


*»«♦-  i S 


iSl"?!  _! 


r 


»\  ' 

ii.V' 


* •ii.iiu,'r-j^i'<>  ^u;>n  r::‘''ii*TT/ (i’f 

O'  'm.  ''■'  - V 

' ^ ^ 'tu^  '■'  ''-vV'V--'  ^ 

U'^  fii>tii-f£o  niki'i/Uttki  ^yu  i 

a:.  '':pffli 

,<viXi*>5:A  < 


i .. 


Lmi 


• «»?■  ai 

<•.  • ^'•.,  • •■*  ■ iMHt^.,-  . .''  , « W-Ji4‘-ar:. . “i  iii  iifl'iiih  ■;  •’;'  ^ (f  ^ 


iL-  i.  ' J ' ' ■.'  <^  "*''X ' ' 


'•  4*?^ 

, ir«iL  ;i4’ 

tn 


.TI' 

- •'•  i\J'  r 

•t  ■ ■ : :.*,.0*  F^v.Jtaw-/;  • . V - .:,.‘';i-;iMB'  'vj 


-Til 

•V  ■•'.>*>  J 'MsV'flj 


' '■'''’^^;f  .W 


.1  T 


V'vi 

0».’  u 

Mm 

..if^ 

t**f.|4 

^ 'i  V 

I.  .'M 


t ■'■  ■' r »' i/«*TO?WW“  t ^ 


My\  y ■■(;.■  ' ■.' . 

[jf  V ..  T^.  ■<  ■ 


Jil®'  W'  A'  Vv}  - ■ 


■*  I /'  4Y4W.ll<il/>  I ,'  ^ 


TABLE  OF  CONTENTS. 


I.  The  Eclipsing  Binary  cr  Aquilae Page  1 

Tables. 

I Observations  of  cr  Aquilae 4 

II  Normal  Magnitudes  of  <r  Aquilae 8 

III  Constants  of  the  Light-Curve 11 

IV  Light-Curve  of  CT  Aquilae 12 

V Spectroscopic  Elements  of  cr  Aquilae 14 

VI  Elements  of  cr  Aquilae, 15 

Figures. 

1 Light-Curve  of  cr  Acjuilae 13 

3 System  of  cr  Aquilae 16 

Summary 17 

II,  The  Cepheid  Variable  op  Aquilae 18 

Tables, 

I Observations  of  op  Aquilae 23 

II  Normal  Magnitudes  of  f3  Aquilae 28 

III  Normal  Magnitudes  of  7 Aquilae.. 29 

IV  Light-Curve  of  7 Aquilae 31 

Figures. 

1 Light-Curve  of  ^ Aquilae 32 

2 Normal  Magnitudes  of  7 Aquilae 33 

3 Variation  in  the  Period  of  7 Aquilae 38 

Summary 40 


I 


;x 


r*  •* 
,1 


v«» 


31 


T)  X'l&dxQ.  s^^XafifioS  «»rf'5. 


•** 


1 V 

X 

- I.-z.vTo^ 

II 

, i J ■ 0 1 w i c aoO 

nx 

^ ' 1/ 

VI 

i .,  .iX 

V ■ 

X>,p. A \-  *;o  7 

. r 

.c^.  IXcpA  "io  avi-  )-4‘agiJ  I 

' ir  ii 


’l^iTJKwS 


''^ai 


t.  I y • 


. . . . ■:  irXiij:.  \ i’l  - bioii-.  0 

' i,yf  c:; 

‘^/'xXrr*  lo  I 

f '.>-' 


X > rj;'  A • >;  '..  ^ .,  '■  i ..  J i;  a^'J.  i iii'/x ;;  /: 

. . . . i i^p  A ; 'i  o f*v  'i  v'j'-yjL  y.iJ 


:r 


V?  *0 

r;jslXL/pA  lo  a:>jti';)’.ti.  V ' ^.  .->1 


i :•  'tc  iotjo^  *f5:Xv  :ii 


YiAya^. 


I.  THE  ECLIPSING  BINARY  SIGMA  AQUILAE. 

The  variable  radial  velocity  of  (TAquilae  (K.  R,  7474, 
magnitude  5,17,  spectrum  B8 ) was  discovered  at  Mt.  Wilson  in  1913, 
and  the  spectroscopic  orbit  was  published  by  Jordan  in  1916,^* 
Jordan  pointed  out  that  the  large  value  of  K suggested  an  eclipsing 
system. 

The  spectra  of  both  components  appear  on  the  plates  of 
this  star.  Eclipsing  binaries  showing  both  spectra  are  the  rare 
and  favorable  oases,  since  by  combining  the  spectroscopic  data  with 
that  from  a good  light-curve  the  dimensions  of  the  system  and  the 
masses  of  the  bodies  can  be  found, 

A short  series  of  photometric  observations  was  made  on 

this  star  by  Dr,  Elmer  Dershem  at  the  University  of  Illinois  in  the 

summer  of  1918,  The  reduction  of  these  showed  variation  in  light, 

which  was  announced  by  Professor  Stebbins  at  the  tv^enty- third  meet- 

2 

ing  of  the  American  AS'tronomical  Society. 

A second  series  of  observations  was  begun  in  June  1930  by 
Professor  Stebbins  and  myself.  This  was  carried  to  the  middle  of 
October  at  which  time  ninety-seven  observations,  about  equally 
divided  between  the  two  observers,  had  been  secured. 

With  two  or  three  exceptions  each  of  these  observations 
is  the  mean  of  three  complete  sets  of  measures,  a set  consisting  of 
two  readings  on  the  comparison  star,  four  on  the  variable,  and  then 
two  more  on  the  comparison  star.  Throughout  the  series,  33 
Aquilae  (H.  R.  7303,  magnitude  5.40,  spectrum  Ao)  was  used  as  the 

^ Publications  of  the  Allegheny  Observatory  3,  189,  1916, 

^ Publications  of  the  American  Astronomical  Society,  4, 
115,  1919.  " 


i',I'i;L,v.  A “v  J'VT  . ::.  .SI.  ^ ^ 

^c*EPPT-  1..'  -:-.w  (.■.■;  ■ o.'  . ,Vi^. . 


..’.'::t  > V«r  b9dliT  u-it  /.tcTT,'  oi':^’OW6'%’ 


I r, . 


r.'-  i ” 


'I 


; i'Ki 


^ , '.'Od 

.’  . .Ti;  :'  ‘,  . ,.• 


• . ' • ; , 'i  ' r 

, 1 ' ' I'j 6 •? .1- • ^ c;::^ ' . ^ 

i>  I 


«■  .'■  ii' — ' ^ 0 fjsl  t „,,  tlO^: 


: ;7::‘:.,.  ,-g<.  v<J  : ,.ti 


J'  , ' I 


C»  a,V3X« 


0 n.  -o 


- r r--:^ 


L 0.1  m * 

L 7<l . - ' 


,.v  I J,,  ' 


A \ 


yd  Cu.-'  i 


. V,  .^i-: 


f 


J 


■ 


I?  r:.-.  ■ 

» ' ■ ' 

;0' . ' ;.;i' 

. ^C.  : .;  ?;  j-tv:3 


V .•..:7,,. 

^ ■.  '< 

:•-.*•’ f lOi  . 

V .^-..  VC  " 

■ d JK 

' 1-; 

• 

■ .:  .t  ::. 

■.■Iraat,  c.^ 

< , 

. jc  ,A'a 

- 

1 

fief‘s* 

. v.?|H 

!>fr, 

i'i 

••  dQ:X  f? 


;<‘.  :>  'lo 


.U  T.  :■•'■  iVcu  . ..  -»  ‘CO 

V*«'M 


#f  *v 


» -f  i.-,  -,  I ' 

^ X V ' ^ — 


■•■'  • %<■ 


• ' •#— ♦»  • — - * - 


■'  Ij  *'-r’  r'it  k -jJ'.U'  ,/•' 


3 


comparison  star. 

The  differential  correction  for  atmospheric  extinction  be- 
tween (T  Aquilae  and  33  Aqullae  was  taken  from  tables  based  on  those 

M 

in  Mdller's  Pho tome trie  der  Qestlrne.  It  was  less  than  0.015  from 

li  h 

sidereal  time  17.4  to  31.0,  and  few  measures  were  taken  outside  this 
limit.  The  correction  to  be  applied  was  determined  by  multiplying 
the  tabular  value  by  a factor  depending  on  the  transparency  of  the 
sky,  which  was  obtained  in  two  ways:  first,  from  the  light  effect  of 
33  Aquilae  on  the  instrument,  corrections  for  instrumental  variation 
having  been  applied;  ajid  second,  from  the  observer's  estimate  at  the 
time  of  making  the  observation.  The  second  method  may  seem  some- 
what crude,  but  the  work  at  this  observatory  indicates  that  the  esti- 
mate of  an  experienced  observer  deserves  about  the  same  weight  as  a 
result  obtained  by  the  first  method.  The  factor  for  each  obser- 
vation was  obtained  by  the  two  independent  methods  and  the  mean  used. 
The  two  stars  are  of  nearly  the  same  spectral  type,  and  as  obser- 
vations with  large  extinction  have  been  rejected  or  given  half  weight, 
errors  due  to  uncertainty  in  this  correction  should  be  small. 

The  times  were  reduced  to  the  sun,  and  the  residuals  from 
an  approximate  light-curve  plotted  using  the  total  atmospheric  ex- 
tinction on  cr Aquilae  as  abscissae.  From  this  plot  of  the  residu- 
als it  was  decided  to  reject  observations  with  an  extinction  greater 

M M 

than  0.35,  Those  with  an  extinction  between  0,18  and  0,35  were 

given  half  weight,  and  a few  which  had  been  marked  weak  for  some 

other  reason,  such  as  smoke,  were  given  weight  one-half  or  three- 

fourths. 

The  center  of  eclipse  was  determined  graphically,  and  from 


‘■ic'^!Kril  ji'lt\%  cKw^a^Ji  ' |R 

■■' >»;i^,'::'^* ;.,;.'/  "■  ■■,■■  .'  v;  '.v.'J-..-  ' <'''C-^"'  r^' 


Pj  , <C.  trf  •■:->’  t i# 


f v3:-.'^<?’*^#ii‘jc  ';-qf  feoij e;#^}ifc*»tf^.i2ftXijfq4  /;»gw  i« 

' la  •-:bhC‘‘r4:^v-i-i If  ^ eUV-  :i0  '>(^1  f 

, ■ '■  . -Al.  ' ^ 

>.  .'  ’ ■ • ,.  ' _'  if.  - •,'  , *<>»■.  ' ' i^'*'-  ' :j 

« 4 ';■<?'»'■  UA'^^?nun‘ff  iO' i<^*-  aAVMcw^’toof 

r<^,  '4’ W:* .«'•.*•  o-'-.a,  f . :fci-tb< ' ' ' 


■|V' &*s/trf.oaW&  3^4^I-,;  • •l5'pri:|*v. 


W - * • » -'  ^ ^ fvJ\  V" 

'iff.,  ^ , /■  .-'  ‘.■;./v  " 'v's^^-'r'  V-r^  ’I 

H'  '■•  '^'  ■ ■ . v.v  . 'V,  .^  ■ . -vi:w  ...  .__X'«-v.;  ^ h 


1 . •tftt;’^r.  f.U  5 V'-Pfv:  A':'?  .’ ‘ •'^* 

]J.':;iar.»‘wift:ii  -s,  -1  , , t4*  ^avah^«i3^<ii»|'V 


. JS 

% 

i! 


►T  i?  Jti  'i .. 


• j.  . 'i/‘*^‘  "i-  I 

offif'’’  ,ViV?  vi\4i^v3t»..  6yl';;e^:;  V 

i:.^^-.;,A/;  ;•  ■;.,  -„\A.'.',*  ,.,  ' ' ''  ? 

..».  >.v,  >■  iitU'A-t.W  •:'.««-“5/-  — .tJ.^i.  . . ‘.  • ^ 


V\  ■ '‘  I '*  ‘*7,  '^i  * ‘ 

'1  '■  •“'  •■  , ,•  ✓•  ■■.,'  'r ' V •'  ■■'  . '' , .'i  ’ 'I  'i,  ■ -^ 

]j 't  . ut-if-')jitir2..fs  .ft^'^‘  ;jtv  - 'si2z6 '^4 ;>X'  'i&v 

1 ;■  X..LFI.  >..■  ■ Mrf.  • ,.■  ••".  .•  >■•'  :*  • • ^ . ...  .•  '■ • 


' .lii® " 

‘ ^ • ■”»  /..r  •■'  .*7.s  V ••.  • •'■'  -.cT*  ■■  ■ •r/>‘^ ' V ■•!***■•  . ^v-;  •.■,?& 


i‘.  ► 


' ti»-Jv:,» 


A\  ’i 


-i-r.-',',-  J^t  VX^'T£ 


ifrir 


3 


the  epoch  of  the  spectroscopic  observations  and  the  1930  photometric 
series  a correction  to  the  Allegheny  period  off 0^00004  was  obtained. 
The  available  observations  in  1918  were  not  sufficient  for  accurate 
determination  of  the  epoch  of  eclipse,  but  a larger  correction  to 
the  Alle^eny  period  would  bring  them  into  better  agreement  with  the 
1930  series. 

A plot  of  the  residuals  with  the  time  as  abscissa  showed 
no  evidence  of  variation  in  the  comparison  star  throughout  the  1930 
series,  but  the  1918  observations  were  systematically  high  by  two 
or  three  hundredths  of  a magnitude.  Because  of  this,  and  the  un- 
certainty in  the  period,  the  few  observations  of  the  earlier  series 
were  omitted  in  the  formation  of  the  normals. 

By  using  the  spectroscopic  period,  with  the  correction  of 
f0f00004  derived  above,  and  the  photometric  determination  of  epoch 
of  eclipse  the  elements 

Minimum  . J.  D.  3433486.797  H-  1^95036‘E 
were  obtained.  These  were  adopted  as  final. 

The  photo-electric  observations  of  (TAquilae  are  given  in 
Table  I.  The  times  were  reduced  to  the  sun,  and  the  phases  com- 
puted from  the  final  elements  given  above.  The  difference  of  magni- 
tude is  the  amount  that  <r  was  measured  brighter  than  33. 

The  observations  of  the  1930  series  were  then  assembled 
according  to  phase  and  grouped  into  normal  magnitudes.  The  rule 
was  in  general  two  observations  to  a normal  during  eclipse  and 
three  to  a normal  outside  of  eclipse.  At  one  phase  outside  of 
eclipse  two  half-weight  observations  taken  on  the  same  night  were 
rejected,  as  the  others  could  be  grouped  into  normals  of  approxi- 


lT*.i 


J, 


^ Si 


v'skiai  ■ -■  , 

©A^Jd3oto4^|  069X  jbna  eno.ttf'J6Vi»acfo  oXqoceOi^ oocja^*  ^ib  Sobac 

.banlMi^io  ex-w  iOOCQ^aylo  lK>i^t©q  ©xl;?  o^  aoXi’oeatob  a adia©© 

* ■■'  " ■ ' ’ • 

lol  iron  03© w 3X61  at  Baot^A^nAgU^  BitSAllavA  a/iT 


*J! 


. V t’  , . I 

aol&nBrttoa  najixjil  a tu^  ^©eqilos'  lo'®£tooq©  ©(if  !to 

9df  rfiiw  od'xii  gnlTb*  />Xjaoi™^oi':^sq  t 

.a»Xi«a-06€X  [Kj. 

bB^odB  -asaioecys  ©a  ©cMi^  4!fi»  iklaxstlz'z^  9dt  \o  ^oXq  A>-  a 
0i.5X  !>£i#  »i/oil8boia3  i*Jb  ae«ix6g3oo  Btf#  gx  naiJaitar  la  •ai£«*i»s  oo  ^ '5 


.-Vv 


"■ 


oy?  ye  yilioX^^o^aya  ciair  caoX3-*v^o3cfo  0X$X  ^i/d" 


fe'' 

'•ajj  ,aXri7  Ip  ©sx/«©©5  .©irr^^Xi^a*  3 Ic  eifi^i>©TbjiSi;tf  tflKflft^'  ^o  |K.^ 

■« 

*f»X*;De  TSilTAd  adtf  lo  6U:Qt&>i7^&BQi>  aiij  at  xtalM&zBo  “« 


I 


*'C 


^i&l^isnoa  Bdf  ho  £toiJtJW530l  ©At^flX 
lo  iioX^siiiico  dstt  ^bct^3q  pXq&wipitoaqa  arfw  ^ias/  y8 

' j"  ■•  gj 

rfcocr©  So  asfitAi'ilm^ftp  oixtm>:otoii(i  90^  bm  b^yrtt^b  K>CQO^Of 

S £ ■’^  ■ g,  ®' 

^ " a^AamsXa  aiqxioa  S%J 
2’3£OdS^X  -f  V8T .33^tBi^^U'*‘.(2'  .^^X^mroci/riK 
■It,  . .I.iatX  03  ibetqpXjA  hrsw  oapfJIJ  , .b^atAi^  ©3^  j 

/Ji  iiavXg  ex»  «AXixfpA”»^  So  oA^i^A^v-rasdo  ttiii’CjaXa-oioiiqt- ‘>tff  J _ 

■ I ' fS6^' 


.I*’^»Xcf3T  \l 


-330  0 8*;'83d^  9d7  bBA  tOUQ  &d7  07  t^OUb^Z  ©iff. 

® ^ t ' ’ 

^iAgAH  So^  ©oa«iaSllJb  atfT  .*©,ycK/3  asvi^  a^taeatl©  X^alS  ■::‘03S.  5aJlrq 

. . .-  .....  ■ ,_ . .' 

.SS 


asd7  z9^si;s.tz(^  bmtf BAom  «©«  ^%,&Ad7  ^mfc^stA  b1  -Smt 

ipJ  ■.  - **  ■■.••■ 


t i/f* 


-i2 


be£dst6B9A  ao4f  b^Itob  0861  »ri^  So  9SOttA7Z9§xio  o41f^, 

® 1 <f  4‘'-" 

sXi/T  edT  .«siHrtiix3ja®  XjBazoa  o^aX  Jboqi/oia.taa  bba^ki  oi’*  i»ai^q|ooo3 


JRS 


^.  ■ '"*•  ' 

Xus«  ©aqiXo©  lumon  a «aoX{fi8vio«db  ow^  Lax9fia%  at  a«v 

*•*  •’ 

.e«qXio5  So  abtBtao  Imzoa  a oi 


Xo^obt24ao  asAdq  oao  tk 

y ■ - ■ !3i 


<now  Jif3ia  emiu©  od^  ao  dadAi  aaot^AVZ^ado  #d3l««^Sl3d -ow^  ieql|oa 
b-lxoiqqa  So  aXasiTOi:  09  if  I b^ttoz^  ad  i»XjUOp  ozadito  s;ft'  ea  »i)3foo^eT 

■ ' u .:  !i  xf:.iE,.  --“:l' 


?r^ 


Tj.iT ' - ir..'’LKy»j^«ag?:.)«R 

I .'  . • - v»  . .'  ’ / ..  ■ - 


a 


f ..I 


;f  i!  "JV. 


ir.'jl  ^<1  a ‘ 


«'-''WiBpy^A:fT»*ya^ 

->V  ■.r'jkl?. 


m 


:) 

•i 


h 


^ .V: 


(V 


I 


,'t 


TABLE  I 


Observations  of  cr Aqui la e 


Date  G.M.T. 

Phase 

Differ- 

Weight 

Date  G.M.T. 

Phase 

Dirf  er- 

Weight 

ence  of 

ence  of 

Magni- 

Magni- 

tude 

tude 

243  2514.737 

0^641 

0^^472 

1918  S« 

CO 

(D 

H 

U 

not  usee 

1) 

2517.711 

1.665 

.426 

1/2 

343  1783.765 

1?017 

0^053 

2521. 768 

1.832 

.423 

i 

1785. 75S 

1.061 

.445 

. 797 

1.851 

.455 

1/2 

1786. 764 

0. 115 

.459 

2532. 711 

0.814 

.438 

1787. 775 

1.134 

.470 

3523.646 

1.749 

(.405) 

1793.738 

1.229 

.470 

.672 

1.775 

.449 

1/2 

1803.771 

0.520 

.497 

2524.679 

0.  833 

.454 

1804.743 

0.541 

.500 

. 733 

0.886 

.425 

1805. 740 

1.539 

.488 

.750 

0.,903 

. 387 

1806.751 

0.600 

.457 

.767 

0.920 

.351 

1813.679 

1.677 

.461 

.783 

0.935 

. 341 

1817.665 

1.763 

.452 

2535.697 

1.850 

•409 

1827.644 

0.040 

. 433 

2526.651 

0.854 

. 430 

1828.649 

1.045 

.411 

. 668 

0.871 

.436 

1837.631 

0.275 

.458 

2538.750 

1.003 

. 349 

1845.611 

0.454 

.468 

3539. 681 

1.934 

. 302 

3530. 615 

0.917 

. 377 

1/2 

1920  S( 

sries 

.637 

0.939 

.338 

2468. 810 

0.017 

. 313 

2531.614 

1.916 

. 300 

1/2 

2498. 774 

0.279 

.474 

.672 

0.024 

. 398 

.840 

0.345 

.465 

2532.643 

0.994 

.315 

2506.763 

0.46S 

.480 

1/2 

.701 

1.053 

. 383 

. 797 

0.502 

.481 

.734 

1.086 

.438 

2508.796 

0.551 

.508 

1/2 

. 751 

1. 103 

.442 

2509.836 

1.581 

. 496 

3535..  615 

O.OIZ. 

1^21. 



,\ 


I 

r 


TABLE  I 

(Contd.  ) 

5 

Date  G.  M.T. 

Pnase 

Dili  er- 
ence  of 
Magni- 
tude 

Weignt 

Date 

G.M. T. 

Phase 

Differ- 
ence of 
Magni- 
tude 

Weigni 

243  25b 5. 629 

0?051 

(0^'^2?4) 

242 

2561. 706 

0?805 

o5|^417 

3/4 

.647 

0.049 

. 298 

1/2 

2566 . 690 

1.887 

. 525 

3/4  1 

. 661 

0.065 

. 528 

5/4 

.708 

1.  905 

.549 

3/4 

.661 

0.  085 

.415 

2567 . 680 

0.  926 

.377 

i 

.692 

0.094 

.402 

.697 

0.945 

. 328 

1/2  1 

.754 

0.  i56 

.452 

2570.619 

1.915 

.315 

. 744 

0.146 

.425 

. 658 

1.954 

.267 

2554.605 

1.005 

. 529 

1/2 

2574.614 

0.059 

. 555 

.619 

1.021 

. 542 

1/2 

.634 

0.079 

. 557 

1/3 

1 

.635 

1 . 055 

.554 

3585. 650 

1.273 

.440 

.694 

1.096 

. 424 

.645 

1.288 

.452 

. 710 

1.112 

.451 

2584.600 

0.  295 

.453 

.724 

1.  126 

.448 

.614 

0.307 

. 455 

2557.710 

0.211 

.475 

3/4 

2585.606 

1.299 

.452 

2539.609 

0. 160 

. 450 

.622 

1.315 

. 448 

.624 

0.175 

. 455 

2587.601 

1.  544 

.436 

j 

2540. 640 

1. 191 

.455 

.615 

1.558 

. 451 

. 658 

1.  209 

. 440 

2588. 592 

0.384 

. 451 

.711 

1.262 

.457 

.605 

0.  597 

. 461 

1 

.722 

1.  275 

. 449 

2589. 574 

1.  566 

.475 

i 

1 

2555. 690 

0.589 

.485 

1/2 

.594 

1.  586 

.446 

2554.647 

1.546 

.457 

2595.594 

1.485 

(.432) 

. 662 

1.561 

. 465 

. 608 

1.  499 

(.424) 

2559.690 

0.758 

.448 

2595. 595 

1.  556 

,473 

. 699 

0.  747 

.447 

.608 

1.  549 

.455 

2561.694 

0.791 

.424 

3/4 

2596 . 554 

0.  544 

. 462 

V-r  * 


* 


! ‘ 
* 

» 


i 

' / 


r 

j 

) 

I 


\ 


TABLii:  I (Cent a. ) 


6 


Date 


342 


G.M.T. 

Phase 

Dirrerence 

of 

Magnitude 

2596. 566 

0^556 

0^^460 

2600.581 

0.671 

. 441 

2603.577 

1.  716 

.430 

.587 

1.726 

.423 

2605.563 

1.  751 

. 441 

.574 

1.762 

. 435 

2606. 514 

0.752 

. 440 

2609. 542 

1.830 

. 422 

.553 

1.841 

.420 

Weignt 


1/3 


7 


mately  the  same  value.  The  thirty-seven  resulting  normal  magni- 
tudes and  the  residuals  from  the  computed  light  curve  are  given  in 
Table  II. 

A plot  of  the  normals  showed  a distinct  ellipticity  effect 
between  minima,  A periastron  effect  might  also  be  suspected,  but 
as  the  spectroscopic  orbit  is  circular,  this  was  considered  error  of 
observation.  There  is  no  appreciable  reflection  effect.  The 
ellipticity  factor  ^ was  obtained  by  Russell's  graphical  method,  and 
the  result  used  to  determine  the  limits  of  the  eclipses  and  check 
the  definitive  work  which  was  as  follows. 

From  normal  magnitudes  outside  of  eclipse  the  ellipticity 
effect  was  solved  for,  using  the  equation: 

m^  — £ cos^^  = ffi 

where  m^denotes  the  maximum  magnitude,  m is  the  observed  magnitude, 

0 is  the  phase  from  primary  minimum,  and  £ is  a constant.  Twenty- 
one  equations  for  the  determination  of  ^ and  £ gave 

m « 0?467  0?0025 

“O 

£ . +0^042  ^ 0^0050 
from  which  z s 0,075, 

The  ellipticity  effect  was  removed  from  the  observations  by  the 
formula 

Rectified  magnitude  * m ^ 0,043  qob^B 
From  a plot  of  the  rectified  magnitudes  at  secondary  minimum  the 
center  of  that  eclipse  was  determined  as  phase  O^’SSO,  from  which 
£ cos  lA)  ■ 40.004,  The  photometric  observations  are  too  few  to 
show  with  certainty  that  the  orbit  is  not  perfectly  circular.  But 
the  eccentricity  of  the  spectroscopic  orbit  is  given  to  only  one 


U-. 

,...  . s>.t  -U.7C 


O.  V .^ 


I 


i!«r)  , 

ll  . V ^ 


■.  r.i’7 


■ .i^-tr-.- 


r ■’  A r.  ^*' 


F'W.r-  ::,li 


I J 


■'■'■Cf  '.'I  :■ 


:■, ex- 


it ’.  7-  '. 


I14  ■«'• 


'u-.  'll 


i 

I 


, j" 


'■  ' nio'i'.  r-y-fC^  ii 


■X 


' - r 1 .:  '7 ...  ■_  < :* : piSik*^. : • 


•'7 2;  " •:  - r.ic 

^ •.  Jt  : ■•■ 


• - ,.ob 


. -C. 


•tv  I; 

’ ' "'r  i 


' Vi  * 


tdv. 


■ •<  I 


« ■■-■■:  I- b^tVtXj  :>9l. 
71  :.' tit::'- o'cn  ' vi;t' 

, . ' &iXT  ^ t rntm.. 

‘i'./'iO,  '-.■'?  r^-;J  7' 


•■‘  . 'j 


■.’> 


7 p.v'V  -i 
*' .■)  .tici  isr 


- V » i 4 

»»  • ••  < 


: 


? ti 


r •*  .f,/ 


t-gtt.gy 


TABLE  II 


Normal  Magnitudes 


Phase 

Dirrer- 

ence 

of 

Magni- 

tude 

Residual 

0-0 

JMO. 

Obs. 

Phase 

Differ- 

ence 

Of 

Magni- 

tude 

Residual 

0-C 

Nc. 

Obs. 

0?020 

M 

0.305 

M 

+0.012 

2 

1.013 

M 

0.  336 

M 

-0. 002 

2 

0.056 

0.323 

-0. 019 

2 

1.044 

0.  368 

-0. 006 

2 

0.069 

0.348 

-0.  017 

2 

1.091 

0.431 

+0.003 

2 

0.088 

0.408 

+0.  010 

2 

1.114 

0.447 

+0.012 

3 

0. 147 

0.429 

-0. 004 

3 

1.200 

0.448 

+0,005 

2 

0.190 

0.451 

+0.012 

2 

1.268 

0.453 

+0.001 

3 

0.  293 

0.461 

+0. 009 

3 

1.280 

0.446 

-0. 008 

2 

0.375 

0.459 

-0. 003 

3 

1.319 

0.445 

-0.013 

3 

0.512 

0.473 

+0.006 

3 

1.370 

0.451 

-0. 012 

3 

0.563 

0.478 

+0.013 

3 

1.  543 

0.462 

-0. 002 

3 

0. 656 

0.  456 

+0. 000 

2 

1.  668 

0.475 

+0.013 

2 

0.742 

0.448 

+0.004 

2 

1.710 

0.426 

-0. 019 

3 

0.779 

0.  428 

-0.011 

3 

1.760 

0.440 

+0.001 

3 

0.833 

0.  44l 

+0. 008 

3 

1.826 

0.422 

-0. 009 

2 

0.878 

0.  426 

+0. 005 

2 

1.848 

0.424 

+0.006 

i 

3 

0.  908 

0.384 

+0. 000 

2 

1.896 

0.337 

-0. 001 

2 

0.923 

0.364 

-0.  002 

2 

1.915 

0.  310 

+0.  000 

2 

0.938 

0.337 

-0.010 

2 

1.934 

0.  294 

+0. 004 

2 

0.998 

0.  332 

+0. 005 

2 

I 


/ 


J, 


. . 


ft; 


I 


t 


9 


decimal,  and  this  value  of  £ cos  wj  seems  possible.  The  obser- 
vations about  secondary  minimum  were  therefore  reflected  about  phase 
©"fsBO  for  further  work. 

From  the  rectified  normals  at  both  primary  and  secondary, 

elements  were  derived  by  Russell's  method.  It  was  found,  however, 

that  as  Russell  has  pointed  out^,  the  value  of  k can  be  determined 

from  partial  eclipses  of  such  small  range  only  with  the  addition  of 

data  other  than  that  derived  from  the  light-curve.  The  assumption 

that  the  eclipses  were  grazing  total  and  annular,  with  k about  0.33, 

gave  the  best  representation  of  the  light-curve.  But  this  means  a 

difference  of  over  two  magnitudes  in  the  light  of  the  components, 

while  from  the  spectroscopic  plates  it  is  known  to  be  much  less. 

The  estimate  published  with  the  spectroscopic  orbit  is  a difference 
M 

of  0.5.  A second  independent  estimate  made  by  Jordan  in  April  1921 
is  0^3. 

The  secoixi  estimate  was  used,  and  from  this,  with  1 -A]_, 

and  1 - Ag  the  photometric  depth  of  minima,  k,  ^ , and  o(^were 

obtained.  After  a few  approximations  the  following  elements  were 

adopted  as  satisfactory, 

X =:  1.70  C =r  0,0799  D ^ 0.0470 

k ■ l.OO(adopted)  1 - ^ = 0,121  1 -A^  - ^*0905 

M 

Rectified  primary  minimum  = 0,327 

M 

Rectified  secondary  minimum  s 0,364 

The  adopted  value  for  k corresponds  to  a difference  of 

0.31  between  the  component  stars,  practically  the  second  estimate. 

M 

Using  k m 0,93  the  light-curve  holds  for  the  first  estimate,  0.5  > 
^Astrophysical  Journal . 35.  331,  1912. 


10 


80  elements  were  computed  for  both  values;  but  the  masses  of  the  com- 
ponent stars,  and  dimensions  and  inclination  of  the  relative  orbit, 
were  found  to  be  practically  the  same  on  the  two  assumptions,  and 
only  the  results  for  k - 1.00  are  given.  An  ephemeris  was  computed 
from  the  adopted  elements  using  Blazko’s  tables^,  and  independently 
by  Russell *8  method  as  a check.  The  computed  light-curve.  Tables 
III  and  IV,  is  shown  in  Figure  1.  The  residuals  from  this  curve 
are  given  in  Table  II,  and  from  these  we  derive 

P.  E.  Single  normal  - ^ 0^06  • 

The  normal  magnitudes  are  plotted  as  circles  in  Figure  1,  the  radius 
of  each  circle  being  equal  to  the  computed  probable  error. 

a 

The  data  of  the  spectroscopic  binary  system  , is  given  in 
in  Table  V.  The  value  of  sin  i.  was  known  from  the  photometric 
elements.  Combining  this  with  the  spectroscopic  elements  the  abso- 
lute dimensions  of  the  system  and  masses  of  the  bodies  were  obtained. 

3 

Following  Russell  , the  apparent  diameter  of  the  brighter  star  was 
computed  from  the  magnitude  and  spectral  type.  From  this  and  the 
actual  diameter,  the  distance  and  parallax  were  obtained,  the  hypo- 
thetical parallax  being  0U006  corresponding  to  a distance  of  about 
550  light  years. 

The  light  elements  are  assembled  in  Table  VI,  and  Figure  3 
is  the  system  represented  by  them.  The  ellipticity  of  the  star 
disks  has  been  neglected  in  the  figure. 

^Annales  de  1 *observatoire  astronomi cue  de  Moscou.  5,  104, 
1911,  o 

Jordan,  Allegheny  Publicati  ons.  3_,  193,  1916. 

^Publications  of  the  Astronomical  Society  of  the  Pacific . 

315,  1920. 


;;/'  :,  -.W''  '.^U' 

«i^aa«»S'  fiidi\iuf^  '^-ffiieriir*  i^Hi^^K'f^jsti' •iite^'4M:'%, ’I 

j(  ',y  , ■ , ^ , 

,en:0‘JS>^Elu!l!ij5^?i’ C:'47t  J!^(t'  HO  «JCf  ;«’' *■ 

■ „;''  ■ ';  . ^’’  . ■ 'ji^v 

ii4‘‘  .aivM'4  :$f^g  rK)^  k t'ti 

- ti  . ’“  r ' * f '"■  * > ' ' ’■'.  f' 

Xlt  tsit^  t dVg^ssiSi^fe  ilriv 


^ , j-air^r.^ ''"'t'  "■  - .•  r*' 

S?7t  aif  ,eX*^t^tiaaii''W'  n|.^;|iS'CaK'  ,^V1 

• ^;i  , ■;  » A<  ' .JJu«.. '^'^lv.  i^i 


*i- 


■ 'it* 


II;-. 4*.^  flat®' *3:43 

1*1^  f 

J 

f.. 


• SOCvOj*  - ^^tux  »i;^i&:  ;s  V|®  ' 


^45^  lJiieiO£'  ;44t’: 


> ';  3 


tX  « ^r.T-f.rsxb*  Id- 'few  twif- 

. !,  ' '■•''■•"■  ' ■■■ . '-j' 

'i -W*  Kdoyi ••  .a«o«?-  1.  n^>tt  f"i5 ,. ; Irti  i'li5X’j^*X.x.i  \ u 


:k 


•/p 


..'t? 


•*o«iS4  of<;’<so£.oTJ 

• "^  . ' ,♦  ‘ , '•N ,-  I \ 

.l>ajU^Cfo  mihnd  TAt  Ic  " ^ a.. 


i£ii»v  %'t7J^3^*35  ejfl  1o  Ta;f i 

rv  • ^ ■ ‘ • t ' 


' ' "W'.,  e.  S ■ ■'  'I'^tiJ '•.  ' 


t 


.v ' , 


II  ' .V  ■ ',  ' ’ '•  • 1^>--  i'^- 

' ^ .unfit  Jq  a v-i3“- i^itjjbc'aa'tfTOc*  &OC^JO-,pn'^dt  xnJMji^q,  £i»o  1,1^3'  - 


8^' 


r-(. 


to  ,IV  ili  9tffikv^U 


ratv  - 

'•ft  A * 


j|v^  Tiavtfe  i)n  t Aoi. 


I 


Vf'vV '.  ('.  , y 


« 


u 


■V  »■' 


,.  .1  \ H'  .■' 


f^_5>ra.v“."l.; 


' r]:  fr'  ’'  . r ':  ' ' ’ 


^^iiobSk-M  V^ii..‘i.'^4i'  -A  X-4tfS?  I'VN’.Uliyti.i.  V -V  ..;  '-y«avfr..’ 


11 


TABLE  III 


Constants  of  tne  Lignt -Curve 


Magnitude 

Range 

Lignt 

Maximum 

0^467 

1.000 

Primary  minimum 

0.285 

M 

0.182 

0.846 

Secondary  minimum 

0.522 

0. 145 

0.875 

Rectified  Curve 

Maximum 

M 

0.467 

— 

1.000 

Primary  minimum 

0.537 

0. 140 

0.879 

Secondary  minimum 

0.564 

0.105 

0.910 

Loss 

0. 154 
0. 125 


0.121 

0.050 


I 

I 


^'V 


©siubB  5ij  et>irJxasjaM  j*)] 

ooo\i  f — ■ :,>'f  ./^  'v 

K * -/  .1  ' ‘ 

d*e.,0  &6I.0  ■-\\'  '25aS' ''O’-,,  '■  j^-,_ 

I.'  I,.-.  itj 


(.  ■ ' 

• ' 


Coo  ,ii. 


fiVfc'.O  ^ OfX  .C  i'vaL^tid!  'a:*! 


7 |, 

Oltt.O  c^X.O  4^t,0 


rw^V'-c 


I ■ .'•»  • ^ ' • r s(  ■ *p  *1.  \ t 

* ' 1 ‘ ♦■ftS  .v^;pW  j.  :4B " * C 

!,  ..t*jLA*&,£tmhi  ..  :>■>'■•■. ft:.ir  ■>  M.'*  -• 


' , ; '*i>-  " ^ ‘.1 


, ./  ^ r;  /:.-:.;V^l^  .. 


y-M 


*; : 


L 


*'j^»JUyjL3tiJue  -■  i>' 


j'A 


13^  , V ' ■\'i\^  ‘ j- • , .'■ ' [i* ' 


I » tsT* 


■■ 


12 


TABLE  IV 
Ligiit-Curve 


Pnase 

Din  erence 

Pnase 

Difference 

of 

of 

Magnitude 

Magnitude 

±ofoo 

M 

0.  285 

0^94 

M 

0.345 

±.0.02 

0.  293 

0.96 

0.328 

±0.04 

0.316 

0.98 

0.322 

±0.06 

0.349 

1.00 

0.328 

±0.08 

0.384 

1.02 

0.345 

±0.10 

0.415 

1.04 

0.370 

±0. 116 

0.430 

1.06 

0.396 

0.15 

0.434 

1.08 

0.419 

0.  20 

0.440 

1.  096 

0.430 

0.30 

0.453 

1.20 

0.443 

0.40 

0.464 

1.30 

0.457 

0.488 

0.467 

1.40 

0.466 

0.60 

0.462 

1.463 

0.467 

0.70 

0.450 

1.50 

0.467 

0.  80 

0.437 

1.60 

0.459 

0.864 

0.430 

1.70 

0.447 

0.88 

0.418 

1.80 

0.434 

0.90 

0.  395 

1.834 

0.430 

0.  93 

0.  369 

14 


TABLE  V 


Spectroscopic  Elerrients  of  CT Aquilae 

(Jordan) 

P 

1?S5032 

±0?-0001  (estimated) 

h 

184? 595 

±0?  0095 

Q 

0.0 

±0.01 

T(Max. Vel . 

)J.D.  2420054.331 

±09^0031 

V 

-5.00  km /sec. 

il.04  km/sec. 

S.1 

163.53  km/sec. 

±0.35  km/sec. 

a]^  sin  ^ 

4,380,000  km 

±3600  km 

m]_  sin'll. 

5. 3 G 

KS 

199  km/sec. 

±4,1  km/sec. 

ap^  sin  i 

5,340,000  km 

±110,000  km 

mp  sin^_i 

4.40 

TABLE  VI 

15 

Elements  of  CT  Aquilae 

1 

1 

1 

Primary  minimum,  J.D. 243 

3486.797  G.M.T. 

1 

Period  of  revolution  (Photometric).  . . . 

P. 

1?95026  1 

Phase  of  secondary  minimum 

0?980 

Semi-duration  of  eclipse 

0?116  j 

Component  of  eccentricity  

^ cos  mj 

+ 0.004 

1 

Cosine  of  inclination  

cos 

0.314 

Ratio  of  radii 

k 

1.00 

1 

Ratio  of  axes  

b/a 

0.955 

Major  semi-axis  

^1=^2 

0.242 

Minor  semi-axis  

0.231 

Light  of  brighter  star 

hi 

0.572 

Light  of  fainter  star  

0.428  ' 

Ratio  of  surface  brightness  

Jl/i2 

1.34 

Magnitude  of  system  

5^*17 

Magnitude  of  brignter  star 

5?78 

Magnitude  of  faini;er  star 

6?09 

From  Allegheny  spectroscopic  elements 

Sun  s= 

1 

Major  semi-axis  

^1=2:3 

3.56 

Minor  semi-axis  

bl=fc3 

3.40 

Density  of  brighter  star 

0.150 

Density  of  fainter  star  

/>2 

0,  125 

Mean  density  of  system 

Po 

0. 138 

Masss  of  brignter  star 

iLi 

6.  19 

Mass  of  fainter  star 

mg 

5.14 

Parallax  (from  surface  brightness^  .... 

TT 

o'.'  006 

fii 


s 


J ■ , 


f: 


1 


I 


r' }.  iU  t'  ^ 


qmaU  Si 


TME  SYSTEM  OF  CT  AQUILAE. 


FIGURE 


Ft- 


< - 


1 


V 


17 


SUMMARY 

1.  A series  of  observations  made  with  a photo-electric 
photometer  during  1930  gives  the  light-curve  of  cr  Aquilae. 

3,  Using  residuals  from  the  computed  curve  the  thlrty- 

4-  M 

seven  normal  magnitudes  show  a probable  error  of  0.006. 

3,  The  comparison  star  32  Aquilae  was  constant  within 
the  limit  of  the  measures  from  July  to  October,  1920,  but  a change 
of  0^?02  between  1918  and  1920  is  indicated  for  either  23  Aquilae 
or  (T  Aquilae, 

4,  Because  of  the  small  range  in  partial  eclipse,  ele- 
ments of  cr  Aquilae  from  the  light-curve  alone  would  be  indetermin- 
ate, but  since  two  spectra  appear  on  the  Allegheny  plates,  the  in- 
formation on  this  eclipsing  system  is  unusually  complete.  The 
elements  and  absolute  dimensions  derived  are  given  in  Table  VI,  and 
the  system  is  shown  in  Figure  3. 


0 V J ' ■ I - •?  7 


V 


j 


♦ 


TT  ^ <»i  •• 


. ■ w 


^:  t;^  • 


. I 


t I 

(•■  «» 


i-i.'  i-.v!'j  wiit?.! 

■ 'W'-^.  J '‘  :- 


11 


U 

t‘ 


18 

II.  THE  CEPHEID  VARIABLE  ETA  AQUILAE. 

A photo-electric  study  of  tj  Aqullae,  one  of  the  best 
known  Cepheid  variables,  was  undertaken  at  the  University  of  Illinois 
in  the  hope  that  something  of  value  might  be  contributed  to  the  dis- 
cussion of  this  type  of  variation.  In  particular,  irregularities 
and  secondary  oscillations  might  be  too  small  for  certain  detection 
by  visual  observers  and  yet  be  conspicuous  in  a photo-electric  light- 
curve  . 

Observations  were  begun  in  July  1930  and  carried  through 
to  November  of  that  year.  In  all  one  hundred  and  eleven  observa- 
tions were  secured,  one  third  by  Professor  Stebbins  and  the  remain- 
der by  myself.  The  variable  and  comparison  stars  are  in  the  Harvard 
system 


H.  R.  7570, 

Aquilae , 

magnitude  3,66-4.45, 

spectrum  G. 

H.  R.  7377, 

S 

Aquilae, 

« 3.44 

« F. 

H.  R.  7603, 

Aquilae , 

" 3,90 

" K. 

The  Mt,  Wilson  spectral  types  are  <>7  Aquilae  F9,  5 Aquilae  A9,  and 
^Aqullae  07.  An  observation  normally  consisted  of  thirty-six 
measures  taken  in  the  following  order 

53,  f36,  73,  ^6,  73,  /36,  73,  ^3, 

one  measure  being  a timing  of  the  rate  of  motion  of  the  electrometer 
thread  between  two  scale  divisions.  Since  S Aquilae  is  brighter 
than  Aquilae,  a neutral  tinted  shade  glass  was  used  to  reduce  the 
light  to  approximate  equality.  Throughout  this  paper  comparisons 
of  other  stars  with  6 Aquilae  should  be  interpreted  as  comparisons 
with  S Aquilae  observed  through  the  shade  glass,  which  reduced  its 
light  about  0^82. 

The  differential  correction  for  atmospheric  extinction 


;JbAIHHTT  .Ul  .11 

S-Btir(f  *ro  2::‘j  ,'nsllifpk  ^ 1o  vJtiL’^a  -o^oc'^i  A. 

u€i:  .iir*.  “iO  vj  iE'T^vi  c j6  Si0h.^tz9l.z:r  bi^rfqaC  xf*ro(T-> 


j -eit  -.r:?  v-J-  lo  :/ Tzd3‘  9qod  »&r 

>0  j.  - XTiXi' -*r  * ^ t *! . *X; ; i~  "i  XKJ  n.  . 'j'.-i.:  l jlV  Xo  Bjtdf-’XO  £iOl9B^'’: 


nojc  ctii’ob  .iLcir’z:>T  icl  I Xaaarf  c i)^  ^.o  34*  in:  it«.Xiioao  VT.:^fcnoo^  i:rr4 

c.^--.^r^-ffi-07  •'.'■c,  £ HL0tr',:.vr.7€'i-  ocf  tf»\  4i.^v-6./cfo  lex/eiv 

uSi/orrf?  tblzziio  l£j:  0S91  '^bt/l  r.i  xiL-^ertf  *^ci^ i^visedO 


» -XSVltQXfO  li-lb.zu..  2,40  I.h  i.T  . ti»t*  ^ ic  TSOffi^VSli;  , 

* . “ 1 

-^.i.^:.■■.s•:  i«n;t  iofi  onirXcf8?B  T :>  i * v*^ s'  i)iid7  ■.  o .i/&i4'-8e  -‘^caw  EX2oif 


i-^.V’TiC'i  arf;f  r.i  x?*;.*:  sa'T  .^teavs  YO 

I 


. .C  vfu 

,ej»SUr-A 

,^>aT  ,H  .H 

nr 
• » 

11 

•S,.  **  f»' 

.1  • *> 

XXx/pA  , k 

t‘^VCV  .fl  .F 

ft 

o 

c 

1 X*  oX  i:.].' a -O, 

tSOo^  .H 

' 'f-'ni 

,t-A  t'aXii/pA 

^^X  • rSbiq^.K  ^ or  A 

'“C-nvo 

sq^:  ,'OsIitT  .; 

xiB-Yr-ii't  xc  \'IL*:r.T4.:  no tex^VT^osjcfo  .VC  ©jeliirpA 

isb':7  '^^-4 ; *.oJ  Xc'i’  ‘'•xfJ  c eti.Ti/axiiK 

.S'-  .V  .'“■■.,?*■  ..r-.-  ,CA.  ,,J  • 

•■  '*  i V 

-5»t c'.xtC'T^vC:'-:! '-  ^,.‘.x  i':;  .'ioiJt;::!  “te  'io  gni"'!?'  .a  r, -ivo  ^msssfe  enc 

■2^-  *. I ,4'*:::  ai  oaiI;jpA  i,  eL'.:tr  . .:,iOJf^ivil>'  sXAoa  oitj  /teav^'scf  bjaaijrfj 
snJ  eaitl5  ate;'&  XjSvt-iif  x.  , T-nXircA  , 

1 

is.ioti x'lxqmco  fLlr,t  .‘rirDii:  . .vi’ifxx^p©  ftt£4rJtXCi.jq-  o7 

sroci'* .-q.ro;>  €0  tvrc'xq're-^.'i  Utl  I ^-voda  3J5li;;pA  :1,U  r<  GXC^fi  lo 

p.7i  r-oot/i-oi  Mof.'iY  ■o.Si^rTe  Lovitacfo  saXiijpA  ?> 

,E;{3^^  i'l/odxi  ifdjjii 

fic-iif on J:rJ5  oi:jS:;^*.'Oirjs:3  ri'oixri&'joo;  ijaiJaeTellib  sdb 


19 


between  7 Aqullae  and  the  comparison  stars  was  taken  from  tables 
based  on  those  in  M<iller*s  Pho tome trie  der  Gestirne.  Nearly  all 
observations  were  within  the  limits  19^^0  and  23^5  sidereal  time, 
during  which  interval  the  maximum  tabular  differential  correction 
was  for  S Aquilae,  0^018,  and  for  Aquilae,  0^043 . The  quantity 

from  the  table  was  multiplied  by  a factor  depending  on  the  trans- 
parency of  the  sky,  which  was  obtained  as  in  the  work  on  cr  Aquilae. 
The  residuals  from  the  preliminary  curve  were  examined  for  a system- 
atic hour  angle  correction;  first,  by  plotting  them  for  nights  on 
which  observations  were  carried  on  throughout  nearly  the  entire  three 
and  a half  hours  during  which  the  star  could  be  observed;  and  second, 
by  comparing  residuals  at  different  hour  angles  on  different  nights, 
using  only  the  best  nights.  There  was  no  indication  of  any  appre- 
ciable systematic  error  remaining  after  the  computed  correction  for 
differential  extinction  has  been  applied,  although  these  corrections 
were  larger  than  is  usual  in  the  work  here. 

The  times  were  reduced  to  the  sun,  and  the  preliminary 
phases  computed  from  the  elements 

Minimum  » J.  D,  2422606.562  -h  7^176382  • E 
The  period  is  that  of  Luizet^,  without  his  harmonic  term.  A plot 
of  the  observations  indicated  that  both  comparison  stars  are  prob- 
ably variable.  At  certain  times  S Aquilae  was  distinctly  faint, 
in  one  case  as  much  as  a tenth  of  a magnitude,  and  toward  the  end  of 
the  series  ^ Aquilae  was  fainter  than  at  the  beginning. 

In  1918  Messrs.  Stebbins  and  Dershem  used  S Aquilae  as 
a comparison  star  for  Nova  Aquilae  No.  3,  and  at  that  time  it  was 

^Astronomische  Nachrichten.  163,  361,  1903. 


liL'Xr.'A?  ,.i 


.r 


aoai-r^'KOO  ed&  btj£:  . xjeeirrf-sd 


IIjp  •{It..-,  .-^  :'--^.t..^O  afrt^.ir:pyorfq  s'^oII/JU  al  stCil^  ixc 

,oaiij-  0^€I  a^iniiX  &.i*3*  Ciid^lXi 

X 

.77i^ ; r *-i.j.".:r£M  ©rf?  X£vt:.?-r:i  dbirlw  tiri-r  . 

^1  . . €s  7 0'1  fc/ . 

?Lf  ;,  v^./j.-naqi-i:  icir-M  A vcf  t-ilfq!:  Xrni  b3u  ©XcfA?  .*1+  ’^oi; 

. :<^o;r  «;’?  rri  ta  X'-' sA«r  -:oiJ>v  ,xit>  "io 

-.-::5.‘c,^  /.  ir''i  ov  r.  ©'viXi-o  v" -A  tialXe-xq  idJ  .’ac^-1  «Xj-.  .,;. ©iil 

^ no  -'■  VO  , c.v i;r ;.-^i-3:i>u  fiX^rw  ut'orf  ct^^J 

r—  ■^'  *n..  L^tzr/^o  i>i9r .,anoX?j?vt©f.tfv  xlot-fw 

,>i:-  : Lr.  ; ‘-.ev- otcj'o  ©itf  Mi/o^i  i.o.?ci  aciaw  \:il^ul  6*ux>d  ^.f«£i  J3 

,?L.:/  :i.7  nx.i.iAllXit  rto  bstliiCL^  ? n 'lo'l-.  .. . eXiit/t  Uo^i  \^a1i-^oiod  ’:c 

V.7,  noiiitoifcxTi  *.ii  otoT,  .?ivJ8i:a  yaatf  ,.Xno  s^iax; 

j 7:':  r..;;.  nos  Clio;.  tad'LXimoc  -on>-  ‘rpi'ro  c ‘:t^o,r.o  + c<70  ©XrfAlo 

■•■  5'  •; 


I 

t / 


V ^•L  v.-t  np;.or:?i-  ,L;^i£qq«  rii-ed  UAid  ’:  ln‘oxiitv&  Xj^ita©TO":'ti.x; 

XlO'  »;1J^  ■'tt  a^di  'X9^z^t  »t©w 

\ni...iT’i*0i£sT^,  x.rta  ^.;ca  nq  Xcoi.'i:.©i-  aioir  drfY 

ni'xrJWi^Xa  mci’y  ' oft^qiaoc*  essAxiq 
:i  « 4-  u , .-iriji  • -. 


t 


.rf 


...i'lO^  oirroAnAC  , ^tsixiuj  lo  botitq  hdT 


CIA  rso.pii^-.-.A  j;;od  t-:i^sotbtil  Mt.oltsv%t^^::o  :>di  io  • 


<.'..  l3l  0',r.  ©Aily;  A J bbicif  r.iAiJ^7©D  . iw'At^.OV  yXuA 

;,.'0  ..-^n  Zy2^V’,)t  ^•'.:  JJ  ^ , j.  rfjjiyjj  ,3,-  ^^0  flX 


i 


u; 


don  Tdiro-.!^"i  ^ eoXiaa  9dt 


or-.  soXio^A  : ..,o:’.  ..n'l  Xfiu:  Oi.iddt-?  ' BX?!  xil  jfj 

3E>i!to  i£  , :'V:  sAX  Jij'pA  jsvo'tl  *io'i  Txs^n  nccXT::.iajoo  ^ 


—I 


# 


20 


suspected  of  variation.  It  has  been  announced  as  a spectroscopic 
3 - 

binary  oi  unknown  period,  and  may  be  an  eclipsing  variable  of  small 
range.  The  other  comparison  star,  p Aquilae,  being  of  spectral 
type  K,  may  be  expected,  if  it  varies  at  all,  to  be  irregular. 

As  a first  step  toward  unravelling  the  variations  of  the 
three  stars,  the  observations  where  8 Aquilae  was  noticeably  faint 
were  marked.  Then  using  only  nights  on  which  the  transparency  of 
the  sky  was  good,  and  including  no  nights  on  which  S Aquilae  had 
been  marked  faint  at  any  time,  the  observed  values  of  p y S were 
plotted  and  a free  hand  curve  dra'^wi.  The  plotted  values  were  com- 
pared with  the  curve,  and  one  or  two  more  rejections  mads  on  the 
ground  that  5 Aquilae  was  perhaps  faint  that  night.  The  remainder 
were  grouped  into  normal  magnitudes  which  are  given  in  Table  II  and 
plotted  in  Figure  1,  From  a free  hand  curve  drawn  through  these 
normal  magnitudes,  the  photo-electric  reduction  of  p Aquilae  to 
S Aquilae  could  be  obtained  for  the  time  of  any  observation. 

The  observed  values  of  p y 8 'wexe  compared  with  this  curve 
and  from  the  residuals  an  unsuccessful  attempt  was  made  to  get  the 
period  of  variation  of  8 Aquilae.  Phases  were  computed  and  the 
residuals  plotted,  at  least  around  the  supposed  minima,  for  several 
different  periods,  but  none  was  considered  satisfactory.  The  range 
of  variation  is  so  small  that  it  is  probably  better  to  await  the  de- 
termination of  the  period  from  spectroscopic  observations. 

Not  knowing  the  variation  of  8 Aquilae,  the  following  ar- 
bitrary rule  was  adopted.  If  any  observed  differed  by  more 

^Astrouhvsical  Journal.  49 , 354,  1919. 

^Lick  Observatory  Bulletin.  2,  126,  1903. 

As trophy si cal  Journal.  39.  265,  1914, 


Pit,  _ - n . r .■ 

llte^agaor  ,1  •- 'ift.-i  t;vT»r-  - r 


r* 


,V.;> 


■c  f i.  Mi-  o::a^  i.;  i:»c  e.^;. 


i 


! 


. aoi;tci’;/sv  iw  j5>etreqot;B 


lii'.UB  1o  5.r-i:jL'i.i:v  n^-  tn,  ^Loiioq  xiTPO/fiuTx/ 

lo  t''  T»£i^o  ®iiT  . 

j . ..j,:  . iTi  :?^  , riij  Sj3  sa2t£V  Cl  li  otjqx©  ■ V"  t ccit* 

/ ”^  • i;; 

f :r;.-'  -’c*  ♦riioXtrisI'X^V  Oa*-  ill® vis^fl*  Ll^WCf^  a®i^S » A:aA 

I :'  • '.'  * ' 

'cIuJrtDi^ :'.i  psr  A vT9iiW  ..anci3^.\rT^&<fo  ,s*r<to^e 

lo  vi>,.oTi:'C:c’ .'lo.M’-'  ua  er.:^in  ^irjfa  nerTT  .LuitAiA 

fci,::  s£lj.,:rpA  ' ioL"'w  :to  fivtrijgic  Oi:  tiACp*’5jt  aj$v  6f:j- 

‘‘■^  •,  ^ .I.“;V  l)ovitv3c'(j  v:  w 4?.-.’',"?  ^is' fc®iT£.-:  rrtecf 

-Y.-^c  ft.  T'-r.toX-;  t.X?  . 'f«r,  to  ^VTifO  o.t./?.*..  o."!  \te  Jt>r..^  6cj?yoIa 

s 

.t  no  i't**'.  ‘ OTO.:  'O  cno  ha?  ^^r'TU'J  d^Lv 

•c»baiAi'-. ..T  ■•:':?  - -t'£u/oi:' 

htJA  II  oXc'iiT  r.i  n»vi^  ei4  dcid'-  'latato.T  b^nl.  Jbtqaois 

.r,:;  ^*'.  •Tr-'nb  3-srr:i.'0  X.-ia.-l  -zzl  h .1  rtX  ,ba^J“oIq 

..  ' '-.ili'. c)..  lo  noi&xiubri^  Dii^'ooXs-c^Oflq  ©dJ-  «';ejL3  , ;t  tn^fc  ?} 

* . i:' avti.-oo  ((ir>  lo  ©ftiX?  . 1i  ’Xo  %>iiXi.Kcfo  '.  . joo  aAlttspA  Z 
dv?:..rr.  •■rXrt3'  A.‘  *'' :. x^i;; ’ .’imij  ^ 6z>jJU\v  b^^rl^^n(^o  s4T 

J»:w  oC"  ffijji,:.  ai’.%  jop;...- ux;  iia  a r.*i;,/jbia©x  tnoil  tn-*? 

s:rt  bas.  . ••t.Ax.Tioo'  im:sv  fe©«s4iX*5  . , 'UJopA  "A  \o  ' do  lo  boll 

ro'i  t-.:i»o.'.Tv'.r«  ?dc  Xnuo’Xta  tOOvO’oXq,  bXax/Msox 

o-'.y.n  e.:'."  .,  ^^i©i»xa;ioo  a>;v/  i’jaon  j'.ra  ^iJioXisq  ,trjOT3'i‘iit 

■•'ji.  ;-ifv  CtBr<J5  oC  X3AJ  vXc.>rioTq  o.i  ji  :t^dC  fXr.iTfO  cX  nci’JiriTav  1*0 
. .4*j  ta‘«vxo<ic^o  ^iqoc^ o'ly  o®q&  r;ox^;  .h0i'isc.  arfi  lo  aoi^imXiKX©^ 
T^nixoIXot'  ode  ^oy,.it:r;z\  >\  lo  rtoX#Jili^>v  6rf:t.  snin^joat  ?o';l 
e^TTr.  11 II  . hi'.-ri?Eao  -p::3  ?wqoh3  b4.w  0X;j'r 


•v’lj 


J 


21 

M r 

than  0.040  from  the  curve  value,  all  comparisons  with  c Aqullae 

M 

were  rejected  on  that  night.  If  no  residual  exceeded  0.040,  hut 

M 

some  exceeded  0.030,  the  observations  on  that  night  were  given  half 
weight.  A few  other  observations  had  already  been  marked  half 
weight  because  of  poor  observing  conditions. 

Observations  of^7'’7were  reduced  to  <5^7^  by  applying  the 
correction  scaled  from  Figure  1.  Normal  magnitudes  for  07  were 
then  formed,  keeping  the  work  on  the  two  comparison  stars  separate  , 
and  a free  hand  curve  drawn.  As  a check,  the  variation  of/oAquilae 
was  then  determined  by  combining  observed  values  of  with  the 

light-curve  of  0^  as  based  on  6 , using  only  good  nights.  These 
computed  values  of  y3  7 5 as  derived  through  07  were  assembled  into 
normal  magnitudes,  which  are  plotted  in  Figure  1 for  comparison  with 
the  values  of  direct  observation.  The  satisfactory  agreement  shows 
that  the  progressive  change  between  p and  S during  the  time  of  ob- 
servation must  be  due  to  a variation  of  /3  , and  that  the  light  vari- 
ation of  07  repeats  itself  from  period  to  period  within  the  limits 
of  the  present  measures. 

The  times  of  maximum  and  minimum,  and  the  amplitude  of 
variation  for  Aquilae  were  derived  graphically  from  the  normal 
magnitudes  as  follows: 

d M 

Maximum,  phase  0.09,  magnitude  -0.501 

Minimum,  phase  5^17,  magnitude  -0^616 

d M 

Maximum  - minimum  2710  > magnitude  1.12 
The  correction  to  the  time  of  maximum  from  the  preliminary  ephemer- 
is  is  thenh0.09.  This  was  applied,  giviig  the  following  elements 
which  were  adopted  as  final: 

d 

Maximum  • J.D.  2422606.652  + 7.176382*  E 


\, 


>/'■> 


I' 

Wii^ 


^ 1.^  ■ J.'.^ 


.’■  -7 


:sr:t  -5 


s .» 


• :,o 


■ r V ' t 


. A" 


K,*.  nV/-'' 


V 4-,  •‘•’I, 


. , |i 


. ^ i. 


•U>:'  i. 


I -• 

- n/  ^ J . . 

i ^ 


•■  ^ i ..fl- 

O'..  •■•.■  (r.rrtyr:: 

I '■  . * J" 

'.,  ■ ■ 


V*' 


n 

V I 


■ r*£ 


^0  ;>'-*v„cv.  > 


• - !< 


:r 


, :■ ' 


4 i 

e * V I 


-r.»,  ■ ’1 


T. 


i -t  fl 


■!-<  ■ 


' r*v  , ofclb 
t ■■•*>■  - 


• ‘ 


V 


’ . ^'  2.  1. 1 } 


OX . <•  „j<w4(£a  - 

•x  ■ <'-:s7  ,.«'C  .U-,  i/.  .••  A“, i o 0| 


. ^ ■' 


•7.asJV^^J 


22 


Table  I gives  the  photo-electric  observations  of  Aquilae. 
The  first  column  gives  the  Greenwich  mean  time  of  observation,  and 
the  second  the  phase  computed  from  the  final  elements;  the  third 
column  gives  the  difference  between  07  Aquilae  direct  and  S Aquilae 
measured  through  the  shade  glass,  and  the  fourth  is  the  measured  dif- 
ference between  07  Aquilae  and  ^ Aquilae,  A positive  sign  means 
in  each  case  that  the  comparison  star  was  brighter  than  op  . Re- 
jected observations  are  in  parentheses,  aind  half  weight  observations 
are  noted  under  remarks.  Since  the  average  time  of  observation  is 
the  same  for  each  star,  the  differences  p brighter  than  S are  ob- 
tained by  subtracting  the  third  column  from  the  fourth. 

The  normal  magnitudes,  with  phases  from  the  final  elements, 
are  given  in  Table  III,  and  plotted  in  Figure  2,  where  points  from 
the  two  comparison  stars  are  kept  separate,  and  the  rejected  S 
Aquilae  observations  are  plotted  as  crosses.  No  p Aquilae  observa- 
tions considered  satisfactory  at  the  time  of  making  have  been  re- 
jected, so  all  comparisons  with  that  star  are  incorporated  in  the 
normal  points. 

The  adopted  light-curve  of  07  Aquilae  is  given  in  Table  IV. 
It  has  not  been  drawn  on  Figure  2 as  the  observations  themselves 
mark  the  course  of  the  curve  satisfactorily.  Further,  anyone  ex- 
amining suspected  fluctuations  will  probably  prefer  a plot  of  the  ob- 
servations free  from  any  evidence  as  to  the  judgment  of  others. 

A glance  at  the  figure  shows  that  the  reality  of  a con- 
siderable "humj?”  cannot  be  questioned.  Since  absolutely  all  of  the 
observations  are  represented  in  Figure  2,  it  is  evident  that  the 
variations  of  p and  ^ do  not  affect  the  establishment  of  this 


St 


J. 


t, 


L^Xlc/pA  to  «rtDj;i"3vi»©cfo  o^s^o«X^'-o^ocf<^A9^Ct  esvig^  r'  eXcfoeT  l^ 

l . -..♦ 


I 


'.ijcw  ,ROX^j8TPi«4id'o  to  itoXtrniiSiO  aovis  iTSttfloo  ^aiXt  eiSt 

B ■ -} 

9£f^  X^jjXt  *201!  jb©i;uqfBjoo  sa 

-i  • '^  •' 

ban  n^ljpk  K-  x»aiftf:acr  aofidT«ltXl>  oii*  aavi^  xlt:{;Xoo 

II  ■ • "' 

i>05X?cii«w  al  arfi  taa  . 

T r '■  ^ 

♦.'M«  aax»  ol'X^iaoq  A .0i*Xt{jp4  tern  ^ naaw^Ad  aoc«Toi  ^ 

-oj^  , HT  T»/^5i*rcf  c^w  xa^a  «toe  1x451000  4oa» 

iffoX^4Ts^»ado  J-Haiaw  !tXjsci  Jbfw  tSoaerJifsox^  aX  er#  aaoXtjsvrtado  ied-oot 


' ai  rtoi^javreacfo  to  auX;f  «oaJ3- 


,«stT^«i  x%tar  bo,roxt  ®f« 
iS*  n ' I 

-cfo  i>TJ3  ir  iM£f^  •:^44^l’i€  e®onoxattx'&  -sfi^  «T4;fs  lot  bom  •J'jf 


■12; 


K 


! I 


t*!<- 


.n?T4«ot  ffloxt  xwjXoo  Ijiisir  e4^  | v 

.B^aoateXo  XaoAi  Boil _ £t4a:lq  a'lfiT*'  X^ritOB  acTJ  ^ ku^ 

«ioit  e;tfi7oq  siujIv  ,S  han  ,UV%1^$T  la  flovXs^l'JB 

..^  AoJotj^ax  od2  i?a^  ,etaxaq^aa  tcrasf  *»xj8  aiita  notxVaqjBoo 

yfi  « /-' 


a 


T 


/•Avxaaoo  OAXiiijpA  oH  -soscotc’ 8oig6s»3’tfoiq  0x4  aaoit^'ntlao’o  ^IXi;pA 
^ D 

-OT  noacf  ®v5:f  to,  aaX;f  Xioxo^teX^Aa  AaxoAisateo  aftoX^ 


i: 

^■j4 


oif;?  zjl  Ao^AToq-xoccX  0X4  xiai*  fiftflW  aac^ix^qajoo  XXji  o«  ,x>«rci®{  j 

,.  .;.>-%•■•■,  j ■ I,  ' 

.VI'  eX3fi-.T  Hi  Havi3  ai  flupXlxipA  to  avxtro-stifcgiX  fco^v.ioii4  arit' ^ 


» V 


aevlotistai^#  ajjolt^vioado  arft  a4  £ mr^xi)  /i03d"^toa  5 


^ -5,8  octo^ffiA  ,x©il^ra/V  .xXixo^cw&tsii^e  otxjo  orl^  te  aaiupa  oili*  Aiao 

^ ■<  ; .n  ' *':Vi|; 

rcfc  o4t  to  ?oXq  * f»tat.T  iXir  BWictJiijtQ^Xt  ^oaqaai  24HiflAfl^ 


,Bi9dtc  to  oiii  ot  60  rorit-l^iT©  aott  aozt  Bnoitf4tT%« 

-noo  4 to  v^iTwot  oxi?  swpjiii  otraXV  ^^4  s^omiXg  A 

i‘:  _,  “ J t 

04f^  to  XX»  vXAx»-4fXo&iA  oo;iiB  ,.A©X2oit«ojjp  e<f  ;^0fl*T40  ♦’cJjsjjrf’^^elo'^TOl^ie 
aiU"  tAiV  tm-£>iaa  aX  pt^llL  at  !!^«^oi^s^«6l'qol  01:4  •aoi^ATi^acfo 

' r/, 

Blitj  to  oxip  J"oott4  tCH  oi>  ^ to  anojt^'#it4Tf| 


tt; 


*u’  " 


Li  ..*‘4'^  7 f A.  ^sid 


n 


,<<j1 


23 

TABLE 

I. 

Obaervations 

of  97  Aquilae 

Difference 

of  Ma^ 

5'nitude 

Date,  G.  M.  T. 

Phase 

8 

(3 

Remarks 

2423523.713 

3?183 

(+0^283) 

,717 

3.187 

+0?345 

.746 

3,216 

(+  .355) 

.751 

3,321 

f .384 

2524.706 

4.176 

+ .448 

+ ,552 

.804 

4.374 

+ .455 

f .566 

2525.765 

5.235 

.588 

+ .680 

2526.711 

6.181 

+ .138 

+ .262 

2528.713 

1.006 

- .280 

- .133 

S half  weight 

.813 

1.106 

- .216 

- .120 

It  n 

2530.761 

3.054 

+ .311 

+ .294 

3532.682 

4.975 

+ .606 

+ .718 

2533.713 

6.006 

+ ,270 

+ .384 

,784 

6.077 

f .189 

+ .283 

2534.661 

6.954 

(-  .566) 

- ,332 

.749 

7.042 

(-  .536) 

- .365 

.801 

7.094 

(-  .500) 

- .420 

2537.739 

2.856 

+ .116 

+ .306 

2538.663 

3.779 

+ .366 

+ .467 

,760 

3.877 

+ ,377 

+ .483 

3539.675 

4.792 

+ .566 

+ .686 

.756 

4.873 

+ .59; 

+ .699 

2540.685 

5.802 

+ .404 

+ .517 

24 


TABLE  I -(continued) 


Difference 

of  Magnitude 

Date,  G,  M.  T. 

Phase 

s 

Remarks 

3422540.742 

5^859 

f0*?364 

f0¥468 

2553.671 

4,435 

(+  .492) 

+ .598 

.729 

4.493 

(+  .456) 

+ .643 

2554 . 604 

5.368 

•J*  .563 

+ .682 

.679 

5.443 

+ .559 

+ .654 

2555.607 

6.371 

+ .005 

+ .136 

2558.786 

2.374 

- .070 

+ ,036 

2559.717 

3.305 

+ .273 

+ .370 

2561.731 

5.319 

+ .597 

+ .681 

3566.622 

3.032 

+ .235 

f .396 

2567.599 

4.009 

+ .383 

+ .506 

S half  weight 

.738 

4.148 

+ .393 

1*  .496 

n R 

2570,594 

7.004 

- .443 

- .381 

.659 

7.069 

- .470 

- .427 

2573.709 

3.943 

+ .106 

+ .220 

S half  weight 

2580.585 

2.642 

- .008 

+ .058 

.689 

2.746 

^ .053 

+ .106 

2583.604 

5.661 

f .499 

+ .549 

.669 

5.726 

+ ,471 

^ .559 

.703 

5.760 

+ .424 

+ .522 

2584.562 

6.619 

- .140 

- .068 

.634 

6.691 

- ,216 

- .147 

. 665 

6.722 

- .278 

- .194 

.694 

6.751 

- .373 

- ,322 

35 


TABLE  I “(continued) 

Difference 
of  Magnitude 


Date,  G.  M.  T. 

Phase 

S 

243585.560 

0^440 

-0^?427 

-0^?363 

.586 

0.466 

- .410 

- .359 

.634 

0.514 

- .414 

- .340 

.649 

0.529 

- .389 

- ,328 

.664 

0.544 

- .377 

- .315 

.679 

0.559 

- .390 

“ .322 

3586.552 

1.432 

(-  .137) 

- .045 

.599 

1.479 

(“  .123) 

1 

« 

o 

♦-* 

.643 

1.523 

(-  .122) 

“ .008 

.685 

1.565 

(-  .119) 

- .044 

2587.560 

2.440 

“ .029 

+ .042 

2588.549 

3.429 

+ .302 

+ .392 

.620 

3.500 

f .291 

f .391 

2593.557 

0.260 

- .472 

“ .378 

.617 

0.320 

- .491 

- .371 

.656 

0.359 

- .511 

“ .362 

.676 

0,379 

- .430 

- .382 

2593.543 

1,346 

- ,082 

.576 

1.279 

(-  .158) 

- .077 

.636 

1.339 

(-  .194) 

- .076 

.660 

1.363 

(-  .151) 

“ ,088 

2594.559 

2.262 

- .033 

.048 

2596.613 

4.316 

+ .465 

.553 

.628 

6.331 

(+  .059) 

4 .081 

Remarks 


(3  half  weight 


Half  weight 


^ half  weight 


I 


26 


TABLE  I -(continued) 

Difference 
of  Magnitude 


Date f G«  M«  T* 

Phase 

S 

2422598.648 

6^351 

(+0^f040) 

+0^f094 

2599.615 

0.141 

- .469 

- .417 

.662 

0.188 

- .500 

- ,398 

2600. 545 

1.071 

- .308 

- .144 

.599 

1.125 

- .188 

- .131 

.644 

1.170 

- .203 

- .135 

2601.569 

2.095 

- .074 

.012 

.590 

2.116 

- .032 

+ .029 

.636 

2.162 

- .068 

+ .002 

.655 

2.181 

- .051 

- ,011 

2603.604 

4.130 

t .433 

+ .498 

2604.633 

5.159 

^ .616 

.690 

2605.526 

6,051 

+ .250 

.342 

.598 

6.123 

+ .191 

* .254 

2606. 537 

7.062 

- .487 

- ,396 

.577 

7.102 

- .495 

- .415 

2607.547 

0.896 

(-  ,304) 

- .220 

.572 

0.921 

(-  ,337) 

- .306 

.589 

0.938 

(-  .315) 

- .178 

2608.544 

1.893 

- .042 

^ ,018 

.-587 

1.936 

- ,054 

+ .015 

.632 

1.981 

- ,084 

- .006 

2609.581 

2.930 

.120 

+ .215 

2614.545 

0.718 

- .346 

- .286 

Remarks 


S half  weight 

II  n 


Half  weight 


u 

r 


t 


\ . 


j’- 


i 

r 


I 


37 


TABLE  I 

“(continued) 

Difference 

of  Magnitude 

Date,  G,  M.  T, 

Phase 

s 

Remarks 

3433615.535 

1^707 

(-o¥055) 

40?011 

.558 

1.730 

(“  .107) 

4 .009 

|3  half  weight 

3618.547 

4.719 

V-  .566 

4 .637 

.587 

4.759 

+ .558 

4 .634 

3619.515 

5.687 

f .481 

4 ,558 

5 half  weight 

.558 

5.730 

4 ,437 

4 ,537 

N n 

3636.553 

5.547 

4 ,543 

4 .609 

3637.540 

6,  534 

- .073 

- ,036 

,558 

6.553 

- .074 

- .033 

3638.543 

0.360 

- .450 

- .367 

.565 

0.383 

- .475 

- .393 

3633.561 

4.379 

4 .505 

4 ,558 

3633.515 

5.333 

4 .588 

4 .648 

3641.535 

6.175 

4 .170 

4 .310 

3643.531 

7.171 

- .485 

- .449 

3649.494 

6.958 

- .433 

- .387 

V 


J. 

•tt 


1 


' *1 

t 


.V  . u 


} 


38 


TABLIl’  1 1 

Normal  Magnitudes  of  ^ Aquilae 


Date  G.M.T.  Dirierence  Number  of 

of  Observations 


Magnitude 


342  25b7.7 

dh06 

7 

3561.7 

. 090 

4 

2582.2 

.076 

4 

2585.2 

. 066 

10 

2600.7 

. 066 

8 

2615.5 

. 065 

1 

2656.0 

.057 

2 

S€ 


f5  ':■'  . 

'.''?flsS  V-5f 

^ jcl'i  , 

‘"‘‘A-,, 

II  aOSAf'  ■' 


^ ^0.  XjmsioH 


g«0i jiivisfc.jo 

\'y 


VdO. 


.<  '■’ 


-i ;,  ■'iv  ,, 

■ • ■ ■A  ■ 


■■  iC  ..'■ 


- ‘ i I'’*  i ' ‘ 


I 


^ . \'Vv;- 


.■.-•^  • 'i  .♦,  , ■ ‘‘1 

''  ir  ■ 


i:?  4fiu 


a^^  vw-ffiST- i-J  1 .■ 


V-M — 


29 


TABLE  III. 

Normal  Magnitudes  of  Aqullae 


Difference 


Difference 


of  Magnitude 

No. 

of  Magnitude 

No. 

Phase 

S 

Obs. 

Phase 

|3(re<^ucec/^ 

Obs. 

0^164 

-o¥484 

-c 

C474 

2 

3^043 

t0^318 

40^^197 

2 

0.313 

- 

.440 

3 

3.204 

4 .250 

2 

0.373 

- 

.463 

2 

3.305 

.273 

,279 

1 

0.374 

- 

.442 

3 

3,464 

,396 

4 .320 

2 

0.473 

- 

.417 

- 

.428 

3 

3.779 

+ 

,366 

4 .362 

1 

0.544 

- 

.385 

~ 

.396 

3 

3.877 

+■ 

,377 

4 ,378 

1 

0.718 

- 

.346 

- 

.347 

1 

4.009 

.383 

4 ,421 

1 

0,918 

- 

.264 

3 

4.136 

+ 

,420 

2 

1.061 

- 

.239 

3 

4.139 

4 .422 

2 

1.064 

,228 

3 

4,176 

-#■ 

.448 

4 .437 

1 

1.148 

- 

.196 

- 

.199 

2 

4.274 

4 

.455 

4 .451 

1 

1.315 

- 

.151 

4 

4.348 

4 

.485 

4 .494 

2 

1.456 

- 

,104 

2 

4.464 

+ .526 

2 

1.544 

- 

.100 

2 

4,739 

4 

,562 

4 .570 

2 

1.715 

- 

.050 

2 

4.832 

4 

.578 

4 ,588 

2 

1.928 

.055 

- 

.051 

3 

4.975 

4 

. 606 

4 .609 

1 

2.124 

- 

.058 

- 

.052 

3 

5.197 

4 

.602 

4 .596 

2 

2.208 

- 

.045 

- 

.058 

2 

5.326 

4 

.592 

4 ,592 

2 

2.407 

- 

.050 

- 

.044 

2 

5.406 

4 

,561 

4 .574 

2 

2.642 

- 

.008 

- 

.019 

1 

5.547 

4 

.542 

4 ,551 

1 

2.746 

.053 

+ 

.029 

1 

5.674 

4 

.490 

4 .486 

2 

2.856 

+ 

.116 

.100 

1 

5.  727 

.460 

2 

2.934 

+ 

.115 

2 

5.728 

4 .481 

2 

2.936 

+ 

.146 

2 

5,760 

4 

.424 

4 .447 

1 

30 


TABLE  III.  -(continued) 


Difference 


Difference 


of  Magnitude 

No. 

of  Magnitude 

No. 

Phase 

S 

(3(rediyced^ 

Obs, 

Phase 

Obs. 

5<?802 

^■0¥404 

f0^413 

1 

6?736 

-0“276 

-0¥283 

2 

5.359 

f .364 

+ .364 

1 

6.956 

- .440 

3 

6.006 

4 .270 

+ ,276 

1 

6.958 

- .422 

1 

6.064 

,320 

^ .236 

3 

7.004 

- .443 

1 

6.133 

4 .191 

f .190 

1 

7.023 

- ,468 

2 

6.178 

^ .154 

.152 

2 

7.064 

- .481 

- .477 

2 

6.355 

.026 

3 

7.123 

- .503 

3 

6.371 

t ,005 

1 

7.136 

- .490 

2 

6.543 

- ,074 

- .086 

3 

6.619 

- .140 

- .143 

1 

6.691 

- .216 

- ,322 

1 

j 

i 

i' 

! 


i 


\ 


.' ' *V  : . 

i 


f 

. » - 
j . .': 

I 

I 


f 


J 


iV 


V~  r 


fA 


;t 

h 


,( 


'i 


V, 


..  w?' 

.uic^;v 


if;4 


. *:l 


31 


TABLE  IV 

Light-Curve  of  ^ Aquilae 


Phase 

Difference 

of 

Magni tude 

Phase 

Difference 

of 

Magnitude 

-2^50 

f0?56 

1^50 

-o¥li 

-2 ,25 

f .60 

1.75 

- .06 

-2.00 

f .61 

2.00 

- ,05 

-1.75 

f .57 

2.25 

- .05 

-1.50 

+ .49 

2.50 

- .03 

-1.25 

t .33 

2.75 

f .03 

-1.00 

t .16 

3.00 

f .21 

-0.75 

.00 

3.25 

f .27 

-0,50 

- .20 

3.50 

4 .31 

-0.25 

- .41 

3.75 

f .36 

0.00 

- .50 

4,00 

4 .40 

+0.25 

- .47 

4.25 

4 .45 

0.50 

- .40 

4.50 

4 ,52 

0.75 

- .33 

4.75 

4 .57 

1.00 

- .24 

5,00 

4 .61 

1.25 

- .17 

5.25 

4 .60 

TSr 


f 


f 


THE  UGHT-CUKVE  OF^  AQUILAE 

6 T] 

o © 


.11 


FI<5U1^E  \. 

DAY5. 

2330  Z550  Z5TO  Z5SO  E6\0  2630 


NORMAL  MAGNITIUDEIS  Of  y)  AQUILAEL^ 


"A  t 

/T\ 

lu  V 

J Q; 

^ O 0 >c 


if) 

1 

O 


(/I 

z 

o 


s 

S f. 

Ui 

O-uJ 

QI^O 
f UJQ 
^tOid 
I^CDh- 

oohi 

9uJ“) 

^Zui 

HOIL 


C$) 


0) 

O). 


<D 


0» 


© <p 


GO 


qt> 

O'  X 


<© 


®0 


00 


© 

© 


KO 

#0 


\9 


>0 


ro 


cs» 


-xG^ 


GD 


o> 


v9 

i:_ 


in 

1’ 


'+• 

j' 


© 


© 


xXx  O 


O 


(0 


cO 


©G>, 


O 


© 


•© 


CNj  yf) 
UJ  >- 

§< 

ij  Q 


(D> 

Od. 


(Of® 
0 ® 


3anj-lN5VU  JQ  30N3y3iJIQ  O© 

(vJ  _ _ CvJ 

r r r U + ■*■  o ■•■* 


'I'- 

+ 


ifi 

4 


vSl 

+ 


nl 

I 


10 

I 


4 


34 


secondary  fluctuation.  Luizet’s^  description  of  the  irregularity, 
”comme  un  arret  dans  la  diminution  d'e^clat  de  la  variable",  or  the 
German  "Stillstand" , fits  the  photo-electric  curve.  The  observa- 
tions indicate  a practically  constant  magnitude  for  about  0?6  be- 

d 

ginning  at  phase  1,8,  Some  of  the  older  curves  from  visual  obser- 
vations show  a pronounced  increase  in  brightness  at  this  point.  It 
was  considered  a real  "secondary  maximum",  but  the  more  recent  light- 
curves  have  been  drawn  with  no  irregularity  in  the  downward  slope" 

The  modern  tendency  is  to  regard  with  suspicion  permanent  Irregu- 

3 

larities  in  curves  by  any  but  the  most  accurate  photometric  methods. 
Photo-electric  work  has  in  general  justified  this  skepticism,  but  in 
this  particular  instance  we  find  confirmation  of  a secondary  oscil- 
lation in  Cepheid  variation,  while  in  addition  to  the  pronounced 
secondary,  there  is  indication  of  another  fluctuation  with  maximum 
about  phase  four  days.  Lockyer  believed  the  irregularities  due  to 
a secondary  oscillation  with  period  1?8,  one-fourth  that  of  the  prin- 
cipal light  variation.  But  it  is  evident  they  cannot  be  represented 
by  a superposing  a simple  sine  curve  of  any  period  on  the  principal 
variation.  Using  Lockyer ‘s  sub-period  we  might  assume  that  the 
secondary  oscillation  rises  to  its  strongest  maximum  about  phase  2?’5, 
A weaker  maximum  is  reached  at  phase  4,3,  the  following  minimum  being 
coincident  with  the  principal  minimum.  The  two  succeeding  second- 
ary fluctuations  are  negligible, 

i 

s tr onomi sc  he  Hachrichten.  165 . 364,  1903. 

^Astronomische  Nachrichten.  183 . 265-78,  1909. 

Mt.  Wilson  Contributions . 7_>  1916. 

Aatronomi sche  Hachrichten,  214.  195,  1921, 

3 

Publications  American  Astronomical  Society,  4,  265,  1921. 


r'  C 


t 


yt 


:c  i' 


i': 


/d. . D.'  ■ X':-  \*:  •i.^nc oaa 


r.h^ifc  L . ■•'I'l/J  'LL'  OBlROG.^ 


-rtv:-; 


;■  ^ “Jtru^c5iIX;?6''  rr£jp.x.-'L( 


IP : . ‘ 

, f 

II  7 


\ 


.2  Zll  Hi  wil-3i‘P.\0  0 . 1{IX  •••.  ..i  .1 0*17'^  : e?AOil:ni  anoXv 

\ '^■'•-tO-  _ .. 

.un":  iif'ViL"?  -'«■*:  Ic»  ud;r  'io -Bas^S  .4^* 


>t.v\::  :-.-  ? :xt  • c.;::X'ac;i.i:  IJOcriJ ';'Cr';  J unoii^v 

■.  " A.,:,oTi  a i)4n,. oieqoc 

. Xv  .X-'-  ■ -.  .irtoi  •)  :t  , : 'Z x.'iJisj.y:  \'it  o.z  di.X7ir  m?.fcTjb  ..-■•-vi’  t fisvuro 

.*.;L,;.,  x . . otr.iyyB  m\5r?3i-  ^4  ai  -\for/.  - ,not!5::x  lirT 

/ 

-;*&«  oiiv'  ;rBOi  ;•  t .yyJ  \,w.  ^:'  aoviiio  .;i  a6i?iigel 


..tfcX 


,i 


■ -vf  ; ‘ liw'OL'.',  X^'rf/19%  flX  aud  XiOf  ciiJ'ooIa-or  f.d'I 
- ••c  i.'.-)  Ji  ;i^X,:  .-s  .1  t^/yob  IsaXi  ow  r^r.^  *j^^uoi^24jq  sixiJ- 

..V.01  . z.'j  o?  *iuirJ  ; .;X  ^i.Xdw  rXi'fvoO  fli  aoljjal 


^x/od-c 

. r : 

i .'.oX2AiXtf3*  \ fc.iOo&t 

‘ T'J-i  , ..ots vdf'XX  Xaqli: 
inig  2X^„,i<j  / r'.rtX'  wqi&q^'g  a vcf 

' , i! 

■ . / 


. :r:::,v,.;..  /- • 

■*  is  - ^:S  ':  1 -^.  ; 

n.:  '>'-C  G;  i. 

? :X  , je'ixX  yC y *■  ■ . v ?:  tX 

' ix  -m.:’  t/o  j 

(«. 

.:  S .i:f -T.^y* -2a<:  , o'7  C xjc 

5'.i;i';- . . t f*' 

So  :P^yj  X^:1S  tt 

r :\'  Xc.;:r^,  yw*^  'to  t : 

vay.  v:^-:  ■•;  • ■ i s t>v.  t.  X '•■•; 

# ' ^ '' 

'V,  -:ix^  r Cr  ;;. 

nX*?'X  .y:u'  X . . 

.-.tHOXIo't  . 

'’  ''S  . , X ■ 1 

cx.  8*.  r^,''Xx«r.  rodiStv?  A 


••91-.  r-i^r>  it lijs  o::t t \,r& 


■*T'  — 

. . 


,iV-4.  . .v^>d0j.7u ay>rsX.-ao::c?TuA 

'X 'lid:2iX2J^-5-l  ' 


5 ■' •'■ 

t i r'O'  *’  - f <7  ^ ( 


i..., ,, 


,)v 


,c>ya  ,J^.  , yy  e tZ03  I-  J.  . ;A 


35 

As  a matter  of  some  interest,  the  light-curve  was  com- 

1 

pared  with  the  velocity  curve  as  determined  toy  Wright.  This  shows 

that  the  pronounced  halt  in  decreasing  light  is  at  apastron  on  the 

"binary  hypothesis,  and  just  before  the  star  reaches  maximum  volume 

on  the  pulsation  hypothesis,  following  Eddington. 

Possible  variation  from  epoch  to  epoch  of  the  light- 

curves  of  this  and  other  Cepheids  has  been  discussed  by  previous 
2 

workers.  The  photo-electric  observations  give  evidence  that  there 
was  no  appreciable  change  in  the  form  of  the  curve  while  the 
observations  were  in  progress,  and  the  curve  is  not  greatly  differ- 
ent from  curves  previously  published  for  this  star.  The  maximum, 
however,  is  somewhat  sharper,  and  the  interval  from  minimum  to 
maximum  light  is  less  than  in  other  recent  curves.  From  the  cuirves 
previously  referred  to  the  values  of  this  interval  were  found  to  be: 
in  1900,  2^38;  1906-07,  2^38;  1917,  2?20;  and  1920,  2^10.  A de- 
cTease  for  the  more  recent  series  is  noticeable,  but  in  all  strict- 
ness comparison  should  be  made  between  curves  determined  with  the 
same  type  of  photometer. 

The  variation  of  the  period  of  y Aquilae  has  also  been 

3 

discussed.  Lockyer,  from  "his  discussion  of  observations  of  the 

4 

past  century,  concluded  it  was  variable,  Luizet  also  found  a vari- 
i~ 

Astrophysical  Journal . £,  62,  1899. 

^Lockyer,  Dissertation,  p.  78-86,  (Gottingen,  1897), 

Luizet,  Astronomische  Nachrichten.  193 . 83,  1913. 

Shapley,  Wilson  Contributions.  £,  179,  1915, 

Jordan,  Publications  American  Astronomical  Society.  4, 

365,  1921. 

3 n 

^Lockyer,  Dissertation,  p.  91,  (Gottingen,  1897). 

Luizet,  Astronomische  Nachrichten.  165.  361,  1903. 


c' 


i<f  r rji- 


t 


'^r:  ■ ..  ..'.'4  Nv'‘'i  ■: 


t '■■■ 


‘ .uT  '.  liT 


■i  4.  ' 


' H 


i'4 


■i  • I.  - 


ktxtr  t {.  - . 


4?'0/ 


,'Ai  ; 

' >•'  :•••■  • ■ •'  -yiy-; ,.  ' 7 t.-ycttV.- 

■ ■■ ' ' i«l  ' 

tail  C ::  • 4. : i ’ 'm-9  -t  . ' - 1 . . 


;ld  ©q  , 


!{'  u:M:,  ‘ 'Xcr  A‘  '.■•■  ‘w:v  i ;rT 


. . '■ 


r.e  .(■#«*»■  ■: 


■ . ^c. 


■ t /- 


«* 


M , 

I. 


3 if  dn-a 


I w , a»M  .(fc. 


, .-.4  .V 


».  ' "•''  < 


. . " . ' ' .'..j,' .,  ■ ■*■1)  ' <'  ^ 

V .. 


* •*  ' 

;0«4 


'(M 


: " ■■'  ' '"•  ■'  J/.'  '(j  ■’•■-i*-"‘ 


■■  >. 


t 

i's 


I -N..  ^ ** 

' , ■*  i »• 


36 


atlon,  and  included  a harmonic  term  in  his  value  for  the  period,  the 

value  which  has  been  used  by  most  observers  of  Aqullae  in  recent 

1 

years.  On  the  other  hand  some  have  rejected  the  harmonic  term. 

The  elements  are 

Maximum  - J.D.  2396168.732  f 7?176382  • E 

^ + 0.14sin(0?044‘E  Jr  304®) 

Maximum  - minimum  • 2,373 

Including  the  harmonic  term  the  epoch  of  maximum  derived  from  the 

photo-electric  curve  gives  as  correction  to  the  ephemeris,  -0,006, 

This  is  good  agreement,  provided  we  go  no  further,  but  for  the 

d, 

minimum  the  correction  is  +0.271,  which  is  not  so  satisfactory, 

A more  accurate  determination  of  the  length  of  the  period 
in  recent  years  was  therefore  made  using  the  photographic  observa- 
tions  of  Kohl sc hut ter"  made  in  1906-07,  The  photographic  and  photo- 
electric amplitudes  being  practically  the  same,  comparison  of  the 
curves  is  direct.  Using  Luizet’s  mean  period  between  the  two  series 
normal  magnitudes  were  formed  from  the  photographic  observations. 
Three  observations  were  combined  in  a normal  point  except  on  the 
steep  portion  of  the  curve  where  two  were  used.  This  steep  portion, 
between  minimum  and  maximum,  was  used  in  the  determination  of  the 
period,  as  the  phase  can  be  determined  with  more  accuracy  here  than 
at  the  time  of  maximum  'or.  minimum, 

A plot  showed  these  points  nearly  a quarter  of  a day  out 
of  phase  with  the  photo-electric  curve,  a graphical  determination 
giving  as  a correction  0,22,  This  gives  as  the  correction  to  the 
period  +0^00032,  from  which  the  value  for  the  period  between  1906 
and  1920  is  7^17670 

^Hellerich,  Dissertation,  p 6,  (Bonn,  1913). 

Astronomische  Nachrichten,  183 . 265,  1909. 


7 w 


i.  - waja--':jtk  ' . , ': 

^ *J 

-:'T  vi^’xy  .,.- 


<50  ■. 

1.r.fx-  fil  g! 

kJ  ■•' 


: ; t ■ ■■ 'r.  oill  . Is 

f « ,~  f . t . ►•'  > 1 1 , . 


, .v' 

r'-'C" 


V ;:>  f-r’y  ' ,r  '.ji<'  : k-j 


V .'h')  'A 


' r ,ii  sa . 

I Z-iy 


:,•  ■ 


?i  lo  u. 


j 


■>:  W'.'*X^  .;•»'*  X i ' 


k.V‘ 


^ ^ t if 

.1 


‘Uv.,  r ■„ 


v.i 


»3WH.  ui?i 


- '..1  /;!  . 


*:ji  btla  :i:tui  j :..t:  .r*s^i»'r/ •.■ . ' 


$A'J  V'l-ni.- 


'■< 


-w 


;'r 


^ ‘ O.Xl  £.<t  (i  ,; 


T ^'i-v 


ftcijo/tn  'ev-,:.  iil  .".'’/feV 


r j ;:i  ^ : , ) X »'j  i rfcf 
i;  .■',*  XK'i  C?v.  0.i  ‘ 


'j  "j:: 


®a*t^  to  li 

1 i" 

-■•  5--  », 

• h . 


.:  j.'tr 


V ' • 


oJttmg:i 


^r-  ■ ; ■ zf  - 


37 

This  value  for  the  length  of  the  period  is  so  much  larger 
than  the  mean  values  of  Lockyer  and  Luizet  obtained  from  a discuss- 
ion of  observations  of  the  past  century  that  Luizet 's  tabulation  of 

i 

coTrections  to  an  ephemeris  from  a constant  period  was  brought  up 
to  date.  Corrections  computed  from  the  light-curves  of 

It  2 

Kohlschutter  and  Lacchini,  and  from  the  photo-electric  light-curve, 
were  added  to  the  list.  These  residuals  are  plotted  in  Figure  3, 
points  from  maxima  and  minima  being  plotted  separately.  Normal 
points  are  formed,  giving  the  determinations  equal  weight  except 
that  in  the  last  point  the  photo-electric  determination  has  been 
given  double  weight.  The  normal  points  are  connected  by  a heavy 
line. 

This  line  is  distinctly  concave  upward,  hence  observa- 
tional evidence  indicates  an  increasing  period  at  least  in  recent 
years.  Certainly  there  is  no  evidence  of  an  appreciable  decrease 
at  any  time  in  the  last  140  years.  If  the  variation  is  harmonic 
the  available  portion  of  the  curve  is  too  little  to  determine 
either  the  amplitude  or  the  period  with  any  accuracy.  However, 
both  must  be  much  greater  than  the  values  found  by  Luizet. 

The  question  of  variation  of  period  is  of  importance  in 

Cepheid  theory.  The  pulsation  hypothesis  demands  a shortening  of 
3 

the  period,  about  40  seconds  annually  for  S Cephei  on  the  con- 
traction theory  of  a star's  energy.  Similar  conclusions  follow  on 
the  rotation  hypothesis,  while  according  to  the  binary  theory  the 


1 

2 

3 


Luizet,  Astronomische  Nachrichten.  163 . 360,  1903, 
Lacchini,  Astronomische  Nachrichten.  214,  195,  1921. 
Eddington,  Observatory.  41,  379,  1918,  339,  1919 


i' 

I' 


.’♦i . . . »'.i  I ,'.’  t ''n 

■»  / ■,^'  xt , >"  a j 9*-  tuxi^ 

V ' ' ' ' ■ -‘  ' 

• ’ •.  • . r..^r:^.*oc  ,a 
. ^:.  :r  .t 


iT^  ixyri 


(j  ‘a 

■ ’ ‘ . \ -/OL  f KVi'.-- 

E?  C5  . . 

. r » 

.-  ‘ * .^TJI  'iS 

. .V  ^ ^ 

M'-Xt.Wji'  41 V It:  /.  . . -** 

' >. 

’ ,,  •»'  f'rril  .s  f ■'  * ,J,-I  ■' 

*4  »..•..  . ' 1.'  1 . 

V < ’ 

^4  ^ «4b«  u*  »JL  ._..  ^‘4  A'  ' 

o.'ii 

ly 

■ -;.  '-t  t'.' 

1} 


; 1 '•> 


\i 


e-.n. 


!, 


. A . * .«i— «t 


7 


» 


^ ... 


.'  -3  V*rr 


t 


•«•  .A*  .fw 


I, " 


variation  \NTH^  PE.RIOD  Of  r]  AQUlLAf 


O 


0 

'i 

k. 


o 

c\l 

9^ 


O 

5\ 


O 

o 

OS 


o 

(f\ 

oQ 


«o 

<0 


<o 


s 

00 


^ If) 
UJ 


<(  S9 
iti 

55 


I 


o 

Si 

«0 


o 

oD 


§ 


sxva 

r*  7-  I-  O I-  7- 


39 

period  may  either  increase  or  decrease!  Tidal  action  should  in 
general  lengthen  the  period  if  it  is  equal  to  or  greater  then  the 
rotation  period  of  the  principal  star.  But  if  the  satellite 
revolves  in  less  than  the  rotation  period,  the  orbital  period 
should  decrease. 

There  is  evidence  that  the  period  of  S Cephel  is 
2 

decreasing.  If  these  suspected  variations  of  period  are  accepted 

as  real  and  attributed  to  tidal  action,  the  deduction  that 

07  Aquilae  probably  rotates  faster  than  6 Cephei  follows. 

Since  either  a rotation  or  a pulsation  should  affect  the 

appearance  of  the  spectral  lines,  the  fact  that  the  lines  of 

'Tj  Aquilae  are  broader  than  those  of  S Cephei  is  wortiy  of  mention, 
^ 3 

6 Cephei  has  the  narrow  well  defined  spectral  lines  typical  of 

4 

giant  stars,  while  the  lines  of  07  Aquilae,  also  classed  with  the 
giant  stars  ”have  the  general  characteristics  of  breadth  and 
haziness,  which  tend  to  make  them  objectionable  for  purposes  of 
accurate  measurement".  In  a footnote  to  this  reference  the 
statement  is  made  that  "There  is  undoubtedly  a resemblance  between 
the  spectra  of  ^7  Aquilae  and  6 Cephei,  the  lines  of  the  latter 
being,  however,  better  defined,  - 
_ 

Plummer,  Monthly  Notices.  80.  507-09,  1920, 

Eddington,  Observatory . 42 . 338,  1919. 

Ludendorff,  Astronomische  Nachrlchten.  312 . 185,  1920, 
^Adams,  Observatory.  43 . 167-68,  1919,  ~ 

^Wright,  Astrophy8icar~Journal . 9,  60,  1899. 


lull 


-V’f:  ■ •■.■•*.’^\:;;j-,  ;,ij 


,^.  SI  sS  i5  it^iiijas 

•■> ^ . * •?■■;''  ■■•  j'  . ’ .■•'  ^ .■  ‘ i-.!^TSsi!  'V~'  f 

v" Wr '-.7 mt ‘ V '^5-  ?7f 3 

. ‘--''t^av  i4i^.M’;..>>  ,A'k;^.u- :'>-;•  ■ ‘ r AiiSt'-,  ^ 

c i‘‘.  ■'  i .■  - ® 


f ^i  A '•■■  /. 


' '’  ' ^ ' ><  E 

li  • E'  tife.v 


i^is 


a;. 


i*?d  'H‘i  i V,J% 


|tTs->sn  1,*^  il  '^'  r.iV*':;  , »''‘-'.r;' ‘ ' ' "*’tV'1 

‘ -lo  »r.‘/::i  •■  i -Vijxlcl*.  "^C-fii 

■' '-  ' i.  . ..f»  ■ » , :'  ' ' iA']J  V 

^9  ''.t.3>r4  SJiS: 


. ''lit 


f'*  T!*'‘  »v  t ^>^.^^bS.‘^'i•^;;^■^?ct.‘' 

-!|i^’'  ' .I  ‘..  Wh'-'i'i'-  . Jii 


sifcv>:r/-  . . •.-. 


- • 'A»i  . I :■  ■»  / , ■ , 


■'*'.  :■  '^  t 


ri,r.i  ■ 

“%v*.  .V'Si  ,i.^i_  '■ 


• ■■"c.km 


tf'  .'';.i'.i*i.  it„S 


TTTji  1 


40 


SlPwIi^ARY 

1 

1.  A series  of  photo-electric  observations  made  in  1930  ! 

gives  an  accurate  light-curve  for  Aquilae. 

i 

3.  The  observations  indicate  a long  period  or  irregular  | 

M 

variation  for  /3  Aquilae.  A progressive  decrease  of  0.05  is  found 
for  an  interval  of  three  months. 

3.  $ Aquilae,  which  has  been  announced  as  a spectro- 

scopic binary  of  unknown  period,  is  suspected  of  being  an  eclipsing 
variable  with  range  about  0?1,  but  no  period  has  been  found. 

4*  The  "secondary  maximum"  in  the  light-curve  of  7 Aquilae 

I 

is  confirmed  as  a pronounced  halt,  or  pause,  in  the  decrease  of  light 
Another  fluctuation,  with  maximum  about  phase  four  days,  is  indicated 

5.  Within  the  accuracy  of  the  measures  the  light-curve  did 
not  change  between  July  and  November  1930.  There  has  perhaps  been 

a shortening  of  the  interval  from  minimum  to  maximum  since  1900,  but 
accurate  curves  determined  with  the  same  photometric  equipment  and 
at  different  epochs  are  needed  for  a thorough  investigation  of  this 
point. 

6.  The  period,  between  1906  and  1930,  is  determined  by 
comparison  with  KohlschiSltter 's  photographic  observations,  Luizet’s 
tabulation  of  residuals  from  the  constant  period  7^176383  is  brought 
up-to-date  by  including  observations  of  1906-07,  1917,  and  1930, 

Both  methods  of  investigation  favor  an  increasing  period  at  present. 
The  evidence  is  decidedly  against  a perceptible  decrease  in  the  peri- 
od at  any  time  since  1784, 

7.  The  pulsation  hypothesis  demands  a shortening  of  the 
period,  while  according  to  the  older  binary  theory,  tidal  action  may 


::.-va5eJ3.j  or.'i  lo  >i 


ic5t  eviuo-irfsil  €iv‘>Jij;/ocMi  sll  tdvis 


*i  i : 1-  bc*i^aq  ^ a;  JiV’.TSacfo  srf' 


! I,'. 


\f 


ic\  ..  - ft 

1: 


• . IdVUSiJCi  £m  Tol 

'.  • '•  * ‘ ,,  V , ' 

• o'i ’■Q^r'9  4*  ^ rioirf'«v  "K 

"io  4 : eZ  tJ^oiTC  ; .'T 5'": j oi<jo  ’- 

. ':  r>'^?c<  iitn  on  cTj.'Co.e  *? -rTr-i  a;;-'  .eXrf,.-liiiv  i 


'to  ;.i  " lO'.Tii.xrfi'  ^liitycrooai*''  *r 


Ih 


il  io  !>r'..  rti  4 j a-  Dv^aiiinoo  2t 


. 1 


- *■  t 


:r  jil'  *i  . o'i  OGJu,’.  ' Tij-:::  ...rxZxja,*?  iTijIw  -leiMi 


ijlr  :';v;.\  - :i;'r  •■'Ot  3 1 iO ' \ ^^TX-’OCiS  ‘ 

^'uoiiT  ..  *-tX  ‘iionu?vo*'  f n^/ *■  - 'fitfid 
\ it 4'/  .v^CrX  60.- oJ"  . ..  ^.*4i;’.  ..rtil  XteVTeTni  ■?  ::^nta'itzo6Q  ~ 

fcrria  fft i;  : .0  oi':?  • inoJ  or.  ’ ?.-a6»s.  Js’/.-ft  to^u'-.o.  n" '.f  . /^uo  oifjyTJL'ooi! 


a;:  ; ':o  c.o i . .s"  ir.  -■v*:i;  /r  ..c'lz a: 


f ..  A 


‘ ij.i.-'  C7  : ^ja 

. .oioq 


t i 


■■  yj-X:.r_Xfr,-ii-  .-V  4j:  ,0Lh’,L  dvQX  notified  ^bOjL-jSii  er^' 


. .io  ^r«v:  ‘ ?’5:.  o ' d^iV3  r^c^XiJsqaoo 


i ^r’':3'L*:d  : 


•'  r ^ 


-n  r*  tr  -r 


r ocf rr.Av ' . : ^^r.t  r^ci'i:  aX^vJtXBOT:  3ro  fto  Z^aXt-'dAi 
Vo  : :\3v-'eado  yd  st.-xj-Ow -qju 

xq  r;  doxooo  -'7  . .i  .u  Xv/Vjit  oo •JbOA'l^sa  /f?cS 

I 

r-.4'j«4  odt  r.t  "■siikOto&^  f. I':’ j ■t  rc'ciDo  -'  •+=■*- ‘ C'v4;  vlbtfli: 'x  t si  V?  ?xfi 

>5VI  oor-.ia  oslv+  <rT^  tii  to 

(ad7  1 0 \ ?:? 3 x:'v9  JL'i  . . : • : .•  7 : , y**  «-  i Ijsa Xitq  ndT  , > 

nclJCMs  L^ciz-  tVxo!jr'j  y-:....J-d  tfi-Ic  t.'-.'  os  n^'il/Jioooja  ei  idvv'  ^thOXTOq  j ] 


41 

increase  or  decrease  the  period.  Other  investigators  have  found 
evidence  of  a decrease  in  the  period  of  S Cephei, 

Either  pulsation  or  rotation  should  affect  the  spectral 
lines  of  a star.  Attention  is  called  to  the  evidence  that  the 
lines  of  Tj  Aquilae  are  broader  than  those  of  S Cephei,  which  have 
been  examined  for  a pulsation  effect. 

ACKNOWLEDGMENT. 

I am  indebted  to  Professor  Joel  Stebbins  for  supervision 
and  direction  throiighout  these  investigations,  and  for  some  of 
the  observational  data,  and  to  Mr.  J.  K.  Willy  for  checking  some 
of  the  reductions. 


•“  " ')  ' ■ ‘ ' HI-'  ''aI»  *5T# 'V 

'■'imfcol  sTC4t4^iiet7ai:  laift’itO  ; ^ 

V'  ^ . C "*  ' 53^-'"  ''’"  ^ ■■■■■  ''-l^ 

■ 6rft;  i i. !»5:’i:«  Li»j{>fi*« ..  t<y  xmitil-  ■ ■'  '*  > . ^-''  ’ ■ ''  '■* 

-■A.  , ' •-.  ■ , ■ fif  "<.,  - ■ ."V"  . “ 


fAY 


" T*>  ►,  /'  ■■  *. . ‘ ■ ' ‘Tf*^ ' * . . ■ I ,•• 

4 lo  RiHiX'S 

r ’ ' '■  * ' ‘,‘"  •^‘  '■%  ,«-.r.  , 

r:ojti®_  tiadviao  A 


& 


^ ^ m''  -:.,M  '3»-^  '"  ■ ■'  f*  ■ ' , •■•'  » - 

CI9C8  i2.'L6 

yf  \ _ ’ ■■  • '_ ^ '■  ''  ■' 


M 


VITA 


Charles  Clayton  Wylie. 

Born  at  Idana,  Kansas,  on  June  18,  1886.  High  school 
education  received  at  Marissa,  Illinois.  Graduated  from  Park 
College,  Parkville,  Missouri,  with  A.  B.  degree  in  1908.  Graduate 
student, as  University  scholar  in  Astronomy, at  the  University  of 
Missouri,  1908-09,  and  summers  of  1909-10;  assistant  and  graduate 
student  1911-13,  receiving  the  A.  M.  deg'ree  in  1913.  Professor  of 
Mathematics,  Buena  Vista  College,  Storm  Lake,  Iowa,  1909-11. 
Assistant,  U.  S.  Naval  Observatory,  Washington,  D,  C.,  1913-19. 
Assigned  to  testing  of  nautical  instruments  1918-19.  Member  of 
U.  S.  Eclipse  Expedition  to  Baker,  Oregon,  June  1918.  Assistant 
and  graduate  student.  University  of  Illinois,  February  1930-1923. 
Married  December  25,  1918, to  Miss  Lirl  Bunn,  Three  Rivers,  Michigan. 

Magazine  articles  published  include:  Determination  of 
the  Longitude  and  Latitude  of  the  U.  S.  Naval  Observatory  Eclipse 
Station  at  Baker,  Oregon,  Popular  Astronomy . 37.  359,  1919;  The 
Auroral  Radiant  from  American  Observations  of  1915-1920,  Terrestrial 
Magnetism  and  Atmospheric  Electricity . 35,  163,  1920;  The  Effect 
of  the  Barometric  Gradient  on  Meridian  Observations,  Popular 
Astronomy.  29 . 479,  1921  (Read  at  the  twenty-fifth  meeting  of  the 
American  Astronomical  Society);  Elements  of  1917  W15,  Astronomical 
Journal . 31.  65,  1918  ( with  E.  C.  Bower);  Second  Elements  and 
Ephemeris  of  1917  W15,  Astronomical  Journal , 65,  1918  (with 

E.C.  Bower). 


